Having reached the end of the Human Genome Project, the question that needs to be asked is: “What... more Having reached the end of the Human Genome Project, the question that needs to be asked is: “What‘s next?”. The complete sequencing of the Human Genome is an immense task, which is now nearing completion. While much work remains to be done even there, there are a number of areas this knowledge opens up to research, which have thus far been nearly impossible to pursue. Among those is “functional genomics” the search for understanding the functionality of specific genes, their relations to diseases, their associated proteins and their participation in biological processes. Most of the knowledge gained so far in this area is the result of painstaking research of specific genes and proteins, based on complex biological experiments and homologies to known genes in other species. This “Reductionist” approach to functional genomics is hypothesis driven (i.e., it can be used to check an existing hypothesis, but not to suggest a new one). The advancements in both biological and computational...
Abstract. In this paper we study the complexity and approximability of the Gc-cut problem. Given ... more Abstract. In this paper we study the complexity and approximability of the Gc-cut problem. Given a complete undirected graph Kn = (V; E) with |V | = n, edge weighted by w(vi, vj) ≥ 0 and an undirected cluster graph, Gc = (Vc, Ec), with |V c | = k, a k-cut is a partition V1,..., Vk of V (G) such that Vi = ∅ for i = 1,..., k. The Gc-cut problem is to compute a k-cut minimizing P w(Vi, Vj) (i,j)∈Ec where w(Vi, Vj) = P p∈V w(p, q). Denote Gc as cluster graph and its vertices as clusters. We i,q∈Vj show that the Gc-cut problem is NP-hard and even not approximable in the general case and remains NP-hard for cluster trees. In particular, we give a complete characterization of hard cases for cluster graphs with at most four vertices by proving that the Gc-cut problem is NP-hard if and only if Gc is isomorphic to 2K2. We also identify some cases where the Gc-cut problem is either polynomial or NP-hard. Finally, we propose polynomial approximation results for the Gc-cut problem when the edge ...
In this paper we study the complexity and approximability of theGc-cut problem. Given a complete ... more In this paper we study the complexity and approximability of theGc-cut problem. Given a complete undirected graph Kn = (V ; E) with |V | = n, edge weighted byw(vi, vj) ≥ 0 and an undirected cluster graph, Gc = (Vc, Ec), with |V c| = k, ak-cut is a partitionV1, . . . , Vk of V (G) such that Vi 6= ∅ for i = 1, . . . , k. TheGc-cut problem is to compute a k-cut minimizing P (i,j)∈Ec w(Vi, Vj) wherew(Vi, Vj) = P p∈Vi,q∈Vj w(p, q). DenoteGc as cluster graph and its vertices as clusters. We show that theGc-cut problem isNP-hard and even not approximable in the general case and remai ns NP-hard for cluster trees. In particular, we give a complete ch aracterization of hard cases for cluster graphs with at most four vertices by proving that the Gc-cut problem isNP-hard if and only ifGc is isomorphic to2K2. We also identify some cases where the Gc-cut problem is either polynomial or NP-hard. Finally, we propose polynomial approximation resul ts for theGc-cut problem when the edge weights ofG ...
Having reached the end of the Human Genome Project, the question that needs to be asked is: “What... more Having reached the end of the Human Genome Project, the question that needs to be asked is: “What‘s next?”. The complete sequencing of the Human Genome is an immense task, which is now nearing completion. While much work remains to be done even there, there are a number of areas this knowledge opens up to research, which have thus far been nearly impossible to pursue. Among those is “functional genomics” the search for understanding the functionality of specific genes, their relations to diseases, their associated proteins and their participation in biological processes. Most of the knowledge gained so far in this area is the result of painstaking research of specific genes and proteins, based on complex biological experiments and homologies to known genes in other species. This “Reductionist” approach to functional genomics is hypothesis driven (i.e., it can be used to check an existing hypothesis, but not to suggest a new one). The advancements in both biological and computational...
Abstract. In this paper we study the complexity and approximability of the Gc-cut problem. Given ... more Abstract. In this paper we study the complexity and approximability of the Gc-cut problem. Given a complete undirected graph Kn = (V; E) with |V | = n, edge weighted by w(vi, vj) ≥ 0 and an undirected cluster graph, Gc = (Vc, Ec), with |V c | = k, a k-cut is a partition V1,..., Vk of V (G) such that Vi = ∅ for i = 1,..., k. The Gc-cut problem is to compute a k-cut minimizing P w(Vi, Vj) (i,j)∈Ec where w(Vi, Vj) = P p∈V w(p, q). Denote Gc as cluster graph and its vertices as clusters. We i,q∈Vj show that the Gc-cut problem is NP-hard and even not approximable in the general case and remains NP-hard for cluster trees. In particular, we give a complete characterization of hard cases for cluster graphs with at most four vertices by proving that the Gc-cut problem is NP-hard if and only if Gc is isomorphic to 2K2. We also identify some cases where the Gc-cut problem is either polynomial or NP-hard. Finally, we propose polynomial approximation results for the Gc-cut problem when the edge ...
In this paper we study the complexity and approximability of theGc-cut problem. Given a complete ... more In this paper we study the complexity and approximability of theGc-cut problem. Given a complete undirected graph Kn = (V ; E) with |V | = n, edge weighted byw(vi, vj) ≥ 0 and an undirected cluster graph, Gc = (Vc, Ec), with |V c| = k, ak-cut is a partitionV1, . . . , Vk of V (G) such that Vi 6= ∅ for i = 1, . . . , k. TheGc-cut problem is to compute a k-cut minimizing P (i,j)∈Ec w(Vi, Vj) wherew(Vi, Vj) = P p∈Vi,q∈Vj w(p, q). DenoteGc as cluster graph and its vertices as clusters. We show that theGc-cut problem isNP-hard and even not approximable in the general case and remai ns NP-hard for cluster trees. In particular, we give a complete ch aracterization of hard cases for cluster graphs with at most four vertices by proving that the Gc-cut problem isNP-hard if and only ifGc is isomorphic to2K2. We also identify some cases where the Gc-cut problem is either polynomial or NP-hard. Finally, we propose polynomial approximation resul ts for theGc-cut problem when the edge weights ofG ...
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Papers by Itamar Elem