Distributed Paging for General Networks

Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, 1993

This paper gives a randomized competitive distributed paging algorithm called Heat & Dump. The competitive ratio is logarithmic in the total storage capacity of the network, this is optimal to within a constant factor. This is in contrast to the linear optimal deterministic competitive ratio BFR92].

Lecture Notes in Computer Science, 1998

Many modern information services know no national boundaries. The widespread use of the Internet and Internet-related applications such as the World Wide Web is growing fantastically on an annual basis. This chapter deals with distributed data management problems. Such problems may arise as a memory management problem for a globally addressed shared memory in a multiprocessor system as well as in a distributed network of processors where data files are kept in different sites and may be accessed for information retrieval by dispersed users and applications. In this context, a file may be a conventional single file, a system database, fragments of a database, or any combination of these. When a processor wishes to access a file it must send a request to a processor holding the file and the desired information is transmitted back. The communication cost incurred thereby is proportional to the distance between the corresponding processors. Files can be replicated and allocated so as to reduce communication costs. Such transactions incur however a high communication cost proportional to the file size times the communication distance. In any case, consistency of the data must be preserved. The main issue in distributed data management is the design of a dynamic allocation of file copies in a network in order to achieve low communication costs. Distributed file assignment problems have been extensively studied in management science, engineering, and computer systems. The 1981 survey paper by Dowdy and Foster [16], compares studies on different models, and cites close to a hundred references. The 1990 paper by Gavish and Sheng [19], gives a survey of recent research on dynamic file assignment problems, where the locations of

Information Processing Letters, 2019

The distributed multi-level multi-server paging problem (DMLMSP) defined in this paper extends and generalizes the classical distributed paging problem [3] to a distributed concurrent multi-level setting, in which multiple servers share caches at multiple levels. The DMLMSP can be used for modeling algorithms for efficient distributed storage systems, in which multiple servers use caches for accelerating access to a centralized storage, maintaining cache coherency across multiple nodes while minimizing access latency and optimizing cache-hit ratio. The DMLMSP model fits basic principles of Non-Uniform Cache Architectures (NUCAs) and can be used for analyzing multiple-level centralized storage. We present an optimal offline algorithm for the DMLMSP model, with minimum number of page faults and minimum makespan, whose time complexity is polynomial in the length of the servers' page request sequences. The new algorithm generalizes and simplifies the state of the art algorithms [3,1].

1991

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2Hk of optimum. (Where Hk is the kth harmonic number, which is roughly Ink.) The best such factor that can be achieved is Hk. This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an on-line algorithm with the optimum off-line algorithm is the idea of comparing it to several other on-line algorithms. We have obtained results along these lines for the paging problem. Given a set of on-line algorithms 'Support was provided by a Weizmann fellowship.

Journal of the ACM, 2012

In the weighted paging problem there is a weight (cost) for fetching each page into the cache. We design a randomized O(log k)-competitive online algorithm for the weighted paging problem, where k is the cache size. This is the first randomized o(k)-competitive algorithm and its competitiveness matches the known lower bound on the problem. More generally, we design an O(log(k/(k − h + 1)))-competitive online algorithm for the version of the problem where the online algorithm has cache size k and the offline algorithm has cache size h ≤ k. Weighted paging is a special case (weighted star metric) of the well known k-server problem for which it is a major open question whether randomization can be useful in obtaining sublinear competitive algorithms. Therefore, abstracting and extending the insights from paging is a key step in the resolution of the k-server problem.

Symposium on the Theory of Computing, 1991

1997

The competitive analysis fails to model locality of reference in the online paging problem. To deal with it, Borodin et al. introduced the access graph model, which attempts to capture the locality of reference. However, the access graph model has a number of troubling aspects. The access graph has to be known in advance to the paging algorithm and the memory required to represent the access graph itself may be very large. In this paper we present truly online strongly competitive paging algorithms in the access graph model that do not have any prior information on the access sequence. We present both deterministic and randomized algorithms. The algorithms need only O(k log n) bits of memory, where k is the number of page slots available and n is the size of the virtual address space. I.e., asymptotically no more memory than needed to store the virtual address translation table. We also observe that our algorithms adapt themselves to temporal changes in the locality of reference. We model temporal changes in the locality of reference by extending the access graph model to the so called extended access graph model, in which many vertices of the graph can correspond to the same virtual page. We define a measure for the rate of change in the locality of reference in G denoted by ∆(G). We then show our algorithms remain strongly competitive as long as ∆(G) ≥ (1 + ε)k, and no truly online algorithm can be strongly competitive on a class of extended access graphs that includes all graphs G with ∆(G) ≥ k − o(k).

Lecture Notes in Computer Science, 1996

In this paper we introduce a generalization of Paging to the case where there are many threads of requests. This models situations in which the requests come from more than one independent source. Hence, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities. Four di erent problems arise whether we consider fairness restrictions or not, with nite or in nite input sequences. We study all of them, proving lower and upper bounds for the competitiveness of on-line algorithms.

Journal of Computer and System Sciences, 1999

In this paper we consider the paging problem when the page request sequence is drawn from a distribution, and give an application to computer networking. In the IP-paging problem the page inter-request times are chosen according to independent distributions. For this model we construct a very simple deterministic algorithm whose page fault rate is at most 5 times that of the best online algorithm (that knows the inter-request time distributions). We also show that many other natural algorithms for this problem do not have constant competitive ratio. In distributional paging the inter-request time distributions may be dependent, and hence any probabilistic model of page request sequences can be represented. We construct a simple randomized algorithm whose page fault rate is at most 4 times that of the best online algorithm. The IP-paging problem is motivation by the following application to data networks. Next generation wide area networks are very likely to use connection-oriented protocols such as Asynchronous Transfer Mode (ATM). For the existing investment in current IP networks such as the Internet to remain useful, we must devise mechanisms to carry IP tra c over connection-oriented networks. A basic issue is to devise holding policies for virtual circuits carrying datagrams; for some connection-oriented networks the holding policy problem is exactly IP-paging.

Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)

In the parallel paging problem, there are p processors that share a cache of size k. The goal is to partition the cache among the processors over time in order to minimize their average completion time. For this long-standing open problem, we give tight upper and lower bounds of Θ(log p) on the competitive ratio with O(1) resource augmentation. A key idea in both our algorithms and lower bounds is to relate the problem of parallel paging to the seemingly unrelated problem of green paging. In green paging, there is an energy-optimized processor that can temporarily turn off one or more of its cache banks (thereby reducing power consumption), so that the cache size varies between a maximum size k and a minimum size k/p. The goal is to minimize the total energy consumed by the computation, which is proportional to the integral of the cache size over time. We show that any efficient solution to green paging can be converted into an efficient solution to parallel paging, and that any lower bound for green paging can be converted into a lower bound for parallel paging, in both cases in a black-box fashion. We then show that, with O(1) resource augmentation, the optimal competitive ratio for deterministic online green paging is Θ(log p), which, in turn, implies the same bounds for deterministic online parallel paging.