The area of computing with uncertainty considers problems where some information about the input ... more The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds.
Presented in STACS 2021. Joint work with Thomas Erlebach and Michael Hoffmann. Supported by EPSRC grant EP/S033483/1.
We study problems with stochastic uncertainty data on intervals for which the precise value can b... more We study problems with stochastic uncertainty data on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time, while finding the data item with minimum value seems to be hard. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.
Video presented in the 14th Latin American Theoretical Informatics Symposium, 5-8 January 2021. Joint work with Steven Chaplick, Magnús M. Halldórsson and Tigran Tonoyan. Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1.
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertain... more We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree problem, a fundamental combinatorial optimization problem that has been central also to the research area of explorable uncertainty. For all integral γ ≥ 2, we present algorithms that are γ-robust and (1+ 1 γ)-consistent, meaning that they use at most γOPT queries if the predictions are arbitrarily wrong and at most (1+ 1 γ)OPT queries if the predictions are correct, where OPT is the optimal number of queries for the given instance. Moreover, we show that this trade-off is best possible. Furthermore, we argue that a suitably defined hop distance is a useful measure for the amount of prediction error and design algorithms with performance guarantees that degrade smoothly with the hop distance. We also show that the predictions are PAC-learnable in our model. Our results demonstrate that untrusted predictions can circumvent the known lower bound of 2, without any degradation of the worst-case ratio. To obtain our results, we provide new structural insights for the minimum spanning tree problem that might be useful in the context of query-based algorithms regardless of predictions. In particular, we generalize the concept of witness sets-the key to lower-bounding the optimum-by proposing novel global witness set structures and completely new ways of adaptively using those. 2012 ACM Subject Classification Theory of Computation → Design and analysis of algorithms Keywords and phrases explorable uncertainty, queries, untrusted predictions
We study problems with stochastic uncertainty information on intervals for which the precise valu... more We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that, for the sorting problem, such a decision tree can be found in polynomial time. For the problem of finding the data item with minimum value, we have some evidence for hardness. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.
Mathematical Foundations of Computer Science, 2019
We study the problem of sorting under incomplete information, when queries are used to resolve un... more We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields the following improved results: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2+O(1/k) if the components obtained have size at least k; and (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also give a randomized adaptive algorithm with query-competitive factor 1 + 4 3 √ 3 ≈ 1.7698 for arbitrary query costs, and we show that the 2-query competitive deterministic adaptive algorithm can be generalized for queries returning intervals and for a more general graph problem (which is also a generalization of the vertex cover problem), by using the local ratio technique. Furthermore, we prove that the advice complexity of the adaptive problem is ⌊n/2⌋ if no error threshold is allowed, and ⌈n/3 • lg 3⌉ for the general case. Finally, we present some graph-theoretical results regarding co-threshold tolerance graphs, and we discuss uncertainty variants of some classical interval problems.
Learning-augmented algorithms have been attracting increasing interest, but have only recently be... more Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For sorting, our algorithm uses the optimal number of queries for accurate predictions and at most twice the optimal number for arbitrarily wrong predictions. For hypergraph orientation, for any γ≥2, we give an algorithm that uses at most 1+1/γ times the optimal number of queries for accurate predictions and at most γ times the optimal number for arbitrarily wrong predictions. These tradeoffs are the best possible. We also consider different error metrics and show that the performance of our algorithms degrades smoothly with the prediction error in all the cases where this is possible.
We study how to utilize (possibly machine-learned) predictions in a model for computing under unc... more We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider fundamental problems such as finding the minima of intersecting sets of elements or sorting them (these problems can also be phrased as (hyper)graph orientation problems), as well as the minimum spanning tree problem. We discuss different measures for the prediction accuracy and design algorithms with performance guarantees that improve with the accuracy of predictions and that are robust with respect to very poor prediction quality. These measures are intuitive and might be of general interest for inputs involving uncertainty intervals. We show that our predictions are PAC learnable. We also provide new structural insights for the minimum spanning tree problem that might be useful in the context of explorable uncertainty regardless of predictions. Our results prove that untrusted predictions can circumvent known lower bounds in the model of explorable uncertainty. We complement our results by experiments that empirically confirm the performance of our algorithms.
In computing with explorable uncertainty, one considers problems where the values of some input e... more In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in the settings where queries are asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. Using competitive analysis, we present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds for the given instance. Given a set of uncertain elements and a family of m subsets of that set, we study the problems of sorting all m subsets and of determining the minimum value (or the minimum element(s)) of each subset. We also study the selection problem, i.e., the problem of determining the i-th smallest value and identifying all elements with that value in a given set of uncertain elements. Our results include 2-round-competitive algorithms for sorting and selection and an algorithm for the minimum value problem The work by Murilo S. de Lima was done while employed at University of Leicester and supported by EPSRC grant EP/S033483/1.
We study how to utilize (possibly machine-learned) predictions in a model for computing under unc... more We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider fundamental problems such as finding the minima of intersecting sets of elements or sorting them (these problems can also be phrased as (hyper)graph orientation problems), as well as the minimum spanning tree problem. We discuss different measures for the prediction accuracy and design algorithms with performance guarantees that improve with the accuracy of predictions and that are robust with respect to very poor prediction quality. These measures are intuitive and might be of general interest for inputs involving uncertainty intervals. We show that our predictions are PAC learnable. We also provide new structural insights for the minimum spanning tree problem that might be useful in the context of explorable uncertainty regardless of predictions. Our results prove that untrusted predictions can circumvent known lower bounds in the model of explorable uncertainty. We complement our results by experiments that empirically confirm the performance of our algorithms.
Modern distributed systems deployed over wireless ad-hoc networks are inherently dynamic and the ... more Modern distributed systems deployed over wireless ad-hoc networks are inherently dynamic and the issue of designing dependable services which can cope with the high dynamics of these systems is a challenge. Byzantine failure detectors provide an elegant abstraction for implementing Byzantine fault tolerance. However, very few works have been proposed for the new distributed system scenario. This paper presents a model and a protocol able to implement an unreliable Byzantine failure detector adequate for dynamic networks with unknown membership. The protocol has the interesting feature to be time-free, that is, it does not rely on timers to detect omission failures. To the best of our knowledge, the adoption of a time-free Byzantine failure detection is novel and this paper provides a first insight towards the understanding and implementation of such an approach in networks with unknown membership.
Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence
Learning-augmented algorithms have been attracting increasing interest, but have only recently be... more Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For sorting, our algorithm uses the optimal number of queries for accurate predictions and at most twice the optimal number for arbitrarily wrong predictions. For hypergraph orientation, for any γ≥2, we give an algorithm that uses at most 1+1/γ times the optimal number of queries for accurate predictions and at most γ times the optimal number for arbitrarily wro...
We study problems with stochastic uncertainty data on intervals for which the precise value can b... more We study problems with stochastic uncertainty data on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time, while finding the data item with minimum value seems to be hard. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting. Although some literature has been devoted to minimizing query/probing costs when solving uncertainty problems with stochastic input, none of them have considered the setting we describe. Our approach is closer to the study of query-competitive algorithms, and it gives a better perspective on the impact of the stochastic assumption.
Given a hypergraph with uncertain node weights following known probability distributions, we stud... more Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge. Querying a node has a cost and reveals the precise weight of the node, drawn from the given probability distribution. Using competitive analysis, we compare the expected query cost of an algorithm with the expected cost of an optimal query set for the given instance. For the general case, we give a polynomial-time f(α)-competitive algorithm, where f(α) ∈ [1.618+e,2] depends on the approximation ratio α for an underlying vertex cover problem. We also show that no algorithm using a similar approach can be better than 1.5-competitive. Furthermore, we give polynomial-time 4/3-competitive algorithms for bipartite graphs with arbitrary query costs and for hypergraphs with a single hyperedge and uniform query costs, with matching lower bounds.
Anais do Encontro de Teoria da Computação (ETC), 2018
In the leasing optimization model, resources are leased for K different time periods, instead of ... more In the leasing optimization model, resources are leased for K different time periods, instead of being acquired for unlimited duration. The goal is to use these temporary resources to maintain a dynamic infrastructure that serves n requests while minimizing the total cost. We propose and study a leasing variant of the online connected facility location problem, which we call the online connected facility leasing problem. In this problem each client that arrives must be connected to a temporary facility, which in turn must be connected to a root facility using permanent edges. We present an algorithm that is O(K · lg n)-competitive if the scaling factor is M = 1.
Resumo. Protocolos tolerantes a faltas são fundamentais no projeto de sistemas distribuídos confi... more Resumo. Protocolos tolerantes a faltas são fundamentais no projeto de sistemas distribuídos confiáveis. Em um sistema distribuído dinâmico, no qual os nós podem entrar e sair da rede aleatoriamente, a qualquer momento da execução do sistema, o desafio de prover tais serviçosé ainda maior. Nesse contexto, um fator preocupante, em especial,é a segurança. Detectores de falhas bizantinas (ou arbitrárias) são uma solução elegante para problemas de segurança, uma vez que separam o tratamento das falhas do protocolo distribuído que os utiliza. No entanto, desconhecem-se trabalhos na literatura descrevendo soluções específicas para sistemas distribuídos dinâmicos. Este artigo propõe um detector de falhas bizantinas para tais sistemas. Adicionalmente, o protocolo apresentadoé assíncrono, istoé, não se baseia no uso de temporizadores para a detecção das falhas, o que favorece sua escalabilidade e adaptabilidade. Tal característica permite com que o protocolo obtido seja naturalmente extensível a um grande número de nós e adaptávelàs diversas variações do ambiente. Palavras-chave: detectores de falhas, falhas bizantinas, sistemas distribuídos dinâmicos, sistemas auto-organizáveis, detectores de falhas assíncronos.
Byzantine failure detectors provide an elegant abstraction for solving security problems. However... more Byzantine failure detectors provide an elegant abstraction for solving security problems. However, as far as we know, there is no complete solution for this problem in a dynamic distributed system. This paper presents thus a first Byzantine failure detector for this context. The protocol has the interesting feature to be asynchronous, that is, the failure detection process does not rely on timers to make suspicions. This characteristic favors its scalability and adaptability.
We study leasing variants of the connected facility location problem, in which we wish to connect... more We study leasing variants of the connected facility location problem, in which we wish to connect a set of clients to facilities, and facilities are connected via core edges, whose cost is a scale factor times the cost of a simple edge. We identify two aspects of the problem that can lead to different variants: (a) if there is a single or multiple commodities, and (b) if we lease facilities and buy core edges, or if we lease both facilities and core edges. Combining these aspects, we propose four variants of the problem, and we give approximation and competitive online algorithms for each of them when the (smallest) scale factor is 1. The algorithms we propose follow the technique of combining available algorithms for the underlying facility leasing and Steiner problems.
The area of computing with uncertainty considers problems where some information about the input ... more The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds.
Presented in STACS 2021. Joint work with Thomas Erlebach and Michael Hoffmann. Supported by EPSRC grant EP/S033483/1.
We study problems with stochastic uncertainty data on intervals for which the precise value can b... more We study problems with stochastic uncertainty data on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time, while finding the data item with minimum value seems to be hard. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.
Video presented in the 14th Latin American Theoretical Informatics Symposium, 5-8 January 2021. Joint work with Steven Chaplick, Magnús M. Halldórsson and Tigran Tonoyan. Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1.
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertain... more We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree problem, a fundamental combinatorial optimization problem that has been central also to the research area of explorable uncertainty. For all integral γ ≥ 2, we present algorithms that are γ-robust and (1+ 1 γ)-consistent, meaning that they use at most γOPT queries if the predictions are arbitrarily wrong and at most (1+ 1 γ)OPT queries if the predictions are correct, where OPT is the optimal number of queries for the given instance. Moreover, we show that this trade-off is best possible. Furthermore, we argue that a suitably defined hop distance is a useful measure for the amount of prediction error and design algorithms with performance guarantees that degrade smoothly with the hop distance. We also show that the predictions are PAC-learnable in our model. Our results demonstrate that untrusted predictions can circumvent the known lower bound of 2, without any degradation of the worst-case ratio. To obtain our results, we provide new structural insights for the minimum spanning tree problem that might be useful in the context of query-based algorithms regardless of predictions. In particular, we generalize the concept of witness sets-the key to lower-bounding the optimum-by proposing novel global witness set structures and completely new ways of adaptively using those. 2012 ACM Subject Classification Theory of Computation → Design and analysis of algorithms Keywords and phrases explorable uncertainty, queries, untrusted predictions
We study problems with stochastic uncertainty information on intervals for which the precise valu... more We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that, for the sorting problem, such a decision tree can be found in polynomial time. For the problem of finding the data item with minimum value, we have some evidence for hardness. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.
Mathematical Foundations of Computer Science, 2019
We study the problem of sorting under incomplete information, when queries are used to resolve un... more We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields the following improved results: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2+O(1/k) if the components obtained have size at least k; and (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also give a randomized adaptive algorithm with query-competitive factor 1 + 4 3 √ 3 ≈ 1.7698 for arbitrary query costs, and we show that the 2-query competitive deterministic adaptive algorithm can be generalized for queries returning intervals and for a more general graph problem (which is also a generalization of the vertex cover problem), by using the local ratio technique. Furthermore, we prove that the advice complexity of the adaptive problem is ⌊n/2⌋ if no error threshold is allowed, and ⌈n/3 • lg 3⌉ for the general case. Finally, we present some graph-theoretical results regarding co-threshold tolerance graphs, and we discuss uncertainty variants of some classical interval problems.
Learning-augmented algorithms have been attracting increasing interest, but have only recently be... more Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For sorting, our algorithm uses the optimal number of queries for accurate predictions and at most twice the optimal number for arbitrarily wrong predictions. For hypergraph orientation, for any γ≥2, we give an algorithm that uses at most 1+1/γ times the optimal number of queries for accurate predictions and at most γ times the optimal number for arbitrarily wrong predictions. These tradeoffs are the best possible. We also consider different error metrics and show that the performance of our algorithms degrades smoothly with the prediction error in all the cases where this is possible.
We study how to utilize (possibly machine-learned) predictions in a model for computing under unc... more We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider fundamental problems such as finding the minima of intersecting sets of elements or sorting them (these problems can also be phrased as (hyper)graph orientation problems), as well as the minimum spanning tree problem. We discuss different measures for the prediction accuracy and design algorithms with performance guarantees that improve with the accuracy of predictions and that are robust with respect to very poor prediction quality. These measures are intuitive and might be of general interest for inputs involving uncertainty intervals. We show that our predictions are PAC learnable. We also provide new structural insights for the minimum spanning tree problem that might be useful in the context of explorable uncertainty regardless of predictions. Our results prove that untrusted predictions can circumvent known lower bounds in the model of explorable uncertainty. We complement our results by experiments that empirically confirm the performance of our algorithms.
In computing with explorable uncertainty, one considers problems where the values of some input e... more In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in the settings where queries are asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. Using competitive analysis, we present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds for the given instance. Given a set of uncertain elements and a family of m subsets of that set, we study the problems of sorting all m subsets and of determining the minimum value (or the minimum element(s)) of each subset. We also study the selection problem, i.e., the problem of determining the i-th smallest value and identifying all elements with that value in a given set of uncertain elements. Our results include 2-round-competitive algorithms for sorting and selection and an algorithm for the minimum value problem The work by Murilo S. de Lima was done while employed at University of Leicester and supported by EPSRC grant EP/S033483/1.
We study how to utilize (possibly machine-learned) predictions in a model for computing under unc... more We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider fundamental problems such as finding the minima of intersecting sets of elements or sorting them (these problems can also be phrased as (hyper)graph orientation problems), as well as the minimum spanning tree problem. We discuss different measures for the prediction accuracy and design algorithms with performance guarantees that improve with the accuracy of predictions and that are robust with respect to very poor prediction quality. These measures are intuitive and might be of general interest for inputs involving uncertainty intervals. We show that our predictions are PAC learnable. We also provide new structural insights for the minimum spanning tree problem that might be useful in the context of explorable uncertainty regardless of predictions. Our results prove that untrusted predictions can circumvent known lower bounds in the model of explorable uncertainty. We complement our results by experiments that empirically confirm the performance of our algorithms.
Modern distributed systems deployed over wireless ad-hoc networks are inherently dynamic and the ... more Modern distributed systems deployed over wireless ad-hoc networks are inherently dynamic and the issue of designing dependable services which can cope with the high dynamics of these systems is a challenge. Byzantine failure detectors provide an elegant abstraction for implementing Byzantine fault tolerance. However, very few works have been proposed for the new distributed system scenario. This paper presents a model and a protocol able to implement an unreliable Byzantine failure detector adequate for dynamic networks with unknown membership. The protocol has the interesting feature to be time-free, that is, it does not rely on timers to detect omission failures. To the best of our knowledge, the adoption of a time-free Byzantine failure detection is novel and this paper provides a first insight towards the understanding and implementation of such an approach in networks with unknown membership.
Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence
Learning-augmented algorithms have been attracting increasing interest, but have only recently be... more Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For sorting, our algorithm uses the optimal number of queries for accurate predictions and at most twice the optimal number for arbitrarily wrong predictions. For hypergraph orientation, for any γ≥2, we give an algorithm that uses at most 1+1/γ times the optimal number of queries for accurate predictions and at most γ times the optimal number for arbitrarily wro...
We study problems with stochastic uncertainty data on intervals for which the precise value can b... more We study problems with stochastic uncertainty data on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time, while finding the data item with minimum value seems to be hard. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting. Although some literature has been devoted to minimizing query/probing costs when solving uncertainty problems with stochastic input, none of them have considered the setting we describe. Our approach is closer to the study of query-competitive algorithms, and it gives a better perspective on the impact of the stochastic assumption.
Given a hypergraph with uncertain node weights following known probability distributions, we stud... more Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge. Querying a node has a cost and reveals the precise weight of the node, drawn from the given probability distribution. Using competitive analysis, we compare the expected query cost of an algorithm with the expected cost of an optimal query set for the given instance. For the general case, we give a polynomial-time f(α)-competitive algorithm, where f(α) ∈ [1.618+e,2] depends on the approximation ratio α for an underlying vertex cover problem. We also show that no algorithm using a similar approach can be better than 1.5-competitive. Furthermore, we give polynomial-time 4/3-competitive algorithms for bipartite graphs with arbitrary query costs and for hypergraphs with a single hyperedge and uniform query costs, with matching lower bounds.
Anais do Encontro de Teoria da Computação (ETC), 2018
In the leasing optimization model, resources are leased for K different time periods, instead of ... more In the leasing optimization model, resources are leased for K different time periods, instead of being acquired for unlimited duration. The goal is to use these temporary resources to maintain a dynamic infrastructure that serves n requests while minimizing the total cost. We propose and study a leasing variant of the online connected facility location problem, which we call the online connected facility leasing problem. In this problem each client that arrives must be connected to a temporary facility, which in turn must be connected to a root facility using permanent edges. We present an algorithm that is O(K · lg n)-competitive if the scaling factor is M = 1.
Resumo. Protocolos tolerantes a faltas são fundamentais no projeto de sistemas distribuídos confi... more Resumo. Protocolos tolerantes a faltas são fundamentais no projeto de sistemas distribuídos confiáveis. Em um sistema distribuído dinâmico, no qual os nós podem entrar e sair da rede aleatoriamente, a qualquer momento da execução do sistema, o desafio de prover tais serviçosé ainda maior. Nesse contexto, um fator preocupante, em especial,é a segurança. Detectores de falhas bizantinas (ou arbitrárias) são uma solução elegante para problemas de segurança, uma vez que separam o tratamento das falhas do protocolo distribuído que os utiliza. No entanto, desconhecem-se trabalhos na literatura descrevendo soluções específicas para sistemas distribuídos dinâmicos. Este artigo propõe um detector de falhas bizantinas para tais sistemas. Adicionalmente, o protocolo apresentadoé assíncrono, istoé, não se baseia no uso de temporizadores para a detecção das falhas, o que favorece sua escalabilidade e adaptabilidade. Tal característica permite com que o protocolo obtido seja naturalmente extensível a um grande número de nós e adaptávelàs diversas variações do ambiente. Palavras-chave: detectores de falhas, falhas bizantinas, sistemas distribuídos dinâmicos, sistemas auto-organizáveis, detectores de falhas assíncronos.
Byzantine failure detectors provide an elegant abstraction for solving security problems. However... more Byzantine failure detectors provide an elegant abstraction for solving security problems. However, as far as we know, there is no complete solution for this problem in a dynamic distributed system. This paper presents thus a first Byzantine failure detector for this context. The protocol has the interesting feature to be asynchronous, that is, the failure detection process does not rely on timers to make suspicions. This characteristic favors its scalability and adaptability.
We study leasing variants of the connected facility location problem, in which we wish to connect... more We study leasing variants of the connected facility location problem, in which we wish to connect a set of clients to facilities, and facilities are connected via core edges, whose cost is a scale factor times the cost of a simple edge. We identify two aspects of the problem that can lead to different variants: (a) if there is a single or multiple commodities, and (b) if we lease facilities and buy core edges, or if we lease both facilities and core edges. Combining these aspects, we propose four variants of the problem, and we give approximation and competitive online algorithms for each of them when the (smallest) scale factor is 1. The algorithms we propose follow the technique of combining available algorithms for the underlying facility leasing and Steiner problems.
We study the problem of sorting under incomplete information, when queries are used to resolve un... more We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive r...
The area of computing with uncertainty considers problems where some information about the input ... more The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds. Given a set of uncertain elements and a family of m subsets of that set, we present an algorithm for determining the va...
Protocolos tolerantes a faltas são fundamentais no projeto de sistemas
distribuídos confiáveis. E... more Protocolos tolerantes a faltas são fundamentais no projeto de sistemas distribuídos confiáveis. Em um sistema distribuído dinâmico, no qual os nós podem entrar e sair da rede aleatoriamente, a qualquer momento da execução do sistema, o desafio de prover tais serviços é ainda maior. Adicionalmente, devido à larga escala de participantes e ao uso comum de comunicação sem fio, não é possível prover aos processos uma visão global da topologia da rede, de forma que cada nó tem um conhecimento parcial da composição do sistema.
Um fator preocupante, em especial, é a segurança, uma vez que a dinamicidade da população dos nós facilita a ação de agentes maliciosos sobre o sistema. O modelo de falhas bizantinas lida com este tipo de ataque assumindo a existência de processos corruptos, que podem se comportar de maneira arbitrária na tentativa de impedir que o sistema funcione conforme a sua especificação. O sistema tolera tais faltas se, apesar do comportamento maligno de alguns de seus processos, ele mantém o seu funcionamento correto.
A abstração de detectores de falhas proposta por Chandra e Toueg provê uma forma modular de tratar as falhas em sistemas assíncronos, separando tal tarefa do protocolo distribuído que os utiliza. Trabalhos recentes foram propostos para implementação da detecção de falhas em sistemas distribuídos dinâmicos, embora nenhum deles lide com a ocorrência de falhas bizantinas. Este trabalho apresenta então um detector assíncrono de falhas bizantinas para sistemas distribuídos dinâmicos. O mesmo baseia-se no detector assíncrono proposto por Sens et al. e na abordagem de detecção de falhas bizantinas descrita por Kihlstrom et al..
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Videos by Murilo de Lima
Presented in STACS 2021. Joint work with Thomas Erlebach and Michael Hoffmann. Supported by EPSRC grant EP/S033483/1.
Keywords: stochastic optimization, query minimization, sorting, selection, online algorithms
Video presented in the 14th Latin American Theoretical Informatics Symposium, 5-8 January 2021. Joint work with Steven Chaplick, Magnús M. Halldórsson and Tigran Tonoyan. Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1.
Papers by Murilo de Lima
Presented in STACS 2021. Joint work with Thomas Erlebach and Michael Hoffmann. Supported by EPSRC grant EP/S033483/1.
Keywords: stochastic optimization, query minimization, sorting, selection, online algorithms
Video presented in the 14th Latin American Theoretical Informatics Symposium, 5-8 January 2021. Joint work with Steven Chaplick, Magnús M. Halldórsson and Tigran Tonoyan. Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1.
distribuídos confiáveis. Em um sistema distribuído dinâmico, no qual os nós podem entrar e sair da rede aleatoriamente, a qualquer momento da execução do sistema, o desafio de prover tais serviços é ainda maior. Adicionalmente, devido à larga escala de participantes e ao uso comum de comunicação sem fio, não é possível prover aos processos uma visão global da topologia da rede, de forma que cada nó tem um conhecimento parcial da composição do sistema.
Um fator preocupante, em especial, é a segurança, uma vez que a dinamicidade da população dos nós facilita a ação de agentes maliciosos sobre o sistema. O modelo de falhas bizantinas lida com este tipo de ataque assumindo a existência de processos corruptos, que podem se comportar de maneira arbitrária na tentativa de impedir que o sistema funcione conforme a sua especificação. O sistema tolera tais faltas se, apesar do comportamento maligno de alguns de seus processos, ele mantém o seu funcionamento correto.
A abstração de detectores de falhas proposta por Chandra e Toueg provê uma forma modular de tratar as falhas em sistemas assíncronos, separando tal tarefa do protocolo distribuído que os utiliza. Trabalhos recentes foram propostos para implementação da detecção de falhas em sistemas distribuídos dinâmicos, embora nenhum deles lide com a ocorrência de falhas bizantinas. Este trabalho apresenta então um detector assíncrono de falhas bizantinas para sistemas distribuídos dinâmicos. O mesmo baseia-se no detector assíncrono proposto por Sens et al. e na abordagem de detecção de falhas bizantinas descrita por Kihlstrom et al..