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Complexity and Applications of EdgeInduced VertexCuts
, 2006
"... Motivated by hypergraph decomposition algorithms, we introduce the notion of edgeinduced vertexcuts and compare it with the wellknown notions of edgecuts and vertexcuts. We investigate the complexity of computing minimum edgeinduced vertexcuts and demonstrate the usefulness of our notion by ..."
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Cited by 2 (0 self)
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Motivated by hypergraph decomposition algorithms, we introduce the notion of edgeinduced vertexcuts and compare it with the wellknown notions of edgecuts and vertexcuts. We investigate the complexity of computing minimum edgeinduced vertexcuts and demonstrate the usefulness of our notion
Subexponential algorithms for Unique Games and related problems
 IN 51 ST IEEE FOCS
, 2010
"... We give subexponential time approximation algorithms for the unique games and the small set expansion problems. Specifically, for some absolute constant c, we give: 1. An exp(kn ε)time algorithm that, given as input a kalphabet unique game on n variables that has an assignment satisfying 1 − ε c f ..."
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Cited by 80 (7 self)
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fraction of its constraints, outputs an assignment satisfying 1 − ε fraction of the constraints. 2. An exp(n ε /δ)time algorithm that, given as input an nvertex regular graph that has a set S of δn vertices with edge expansion at most ε c, outputs a set S ′ of at most δn vertices with edge expansion
Approximation Algorithms for Maximization Problems arising in Graph Partitioning
, 1998
"... Given a graph G = (V; E), a weight function w : E ! R + and a parameter k we examine a family of maximization problems arising naturally when considering a subset U ` V of size exactly k. Specifically we consider the problem of finding a subset U ` V of size k that maximizes : MaxkVertex Cover ..."
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Cited by 55 (5 self)
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: the weight of edges incident with vertices in U . MaxkDense Subgraph : the weight of edges in the subgraph induced by U . MaxkCut : the weight of edges cut by the partition (U; V n U ). MaxkNot Cut : the weight of edges not cut by the partition (U; V n U ). We present a number of approximation
Approximating Clique and Biclique Problems
, 1998
"... We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges de ..."
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Cited by 44 (2 self)
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We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges
Grid vertexunfolding orthogonal polyhedra
 IN PROC. 23RD SYMPOS. THEORET. ASPECTS COMPUT. SCI., LECTURE NOTES COMPUT. SCI
, 2006
"... An edgeunfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces in t ..."
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Cited by 4 (1 self)
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An edgeunfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces
On the Equivalence of the Bidirected and Hypergraphic Relaxations for Steiner Tree
"... The bottleneck of the currently best (ln(4)+ε)approximation algorithm for the NPhard Steiner tree problem is the solution of its large, so called hypergraphic, linear programming relaxation (HYP). Hypergraphic LPs are NPhard to solve exactly, and it is a formidable computational task to even appr ..."
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to be close to the real answer, only a (trivial) upper bound of 2 is known. In this paper, we give an efficient constructive proof that BCR and HYP are polyhedrally equivalent in instances that do not have an (edgeinduced) claw on Steiner vertices, i.e., they do not contain a Steiner vertex with 3 Steiner
Tutte's 3Flow Conjecture and Matchings in Bipartite Graphs
, 2001
"... Tutte's 3flow conjecture is restated as the problem of nding an orientation of the edges of a 4edgeconnected, 5regular graph G, for which the outflow at each vertex is +3 or 3. The induced equipartition of the vertices of G is called mod 3orientable. We give necessary and sufficient ..."
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Cited by 2 (0 self)
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Tutte's 3flow conjecture is restated as the problem of nding an orientation of the edges of a 4edgeconnected, 5regular graph G, for which the outflow at each vertex is +3 or 3. The induced equipartition of the vertices of G is called mod 3orientable. We give necessary and sufficient
Spanning Eulerian Subgraphs in clawfree graphs
"... A graph is clawfree if it has no induced K1,3 subgraph. A graph is essential 4edgeconnected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4edgeconnected claw free graph has a spanning Eulerian subgraph with ..."
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Cited by 1 (1 self)
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is essentially kedgeconnected if for any X ⊆ E(G) with X  < k, at most one component of G − X has edges. The line graph L(G) of a graph G has E(G) as its vertex set and two vertices of L(G) are adjacent if and only if they are adjacent as edges in G. A graph is called clawfree if it has not induced
The Generalized Subgraph Problem: Complexity, Approximability and Polyhedra
, 2003
"... This paper is concerned with a problem on networks which we call the Generalized Subgraph Problem (GSP). The GSP is defined on an undirected graph where the vertex set is partitioned into clusters. The task is to find a subgraph which touches at most one vertex in each cluster so as to maximize the ..."
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the sum of vertex and edge weights. The GSP is a relaxation of several important problems of a ‘generalized’ type and, interestingly, has strong connections with various other wellknown combinatorial problems, such as the quadratic semiassignment, maxflow / mincut, matching, stable set, uncapacitated
StrongDiameter Decompositions of Minor Free Graphs
, 2007
"... We provide the first sparse covers and probabilistic partitions for graphs excluding a fixed minor that have strong diameter bounds; i.e. each set of the cover/partition has a small diameter as an induced subgraph. Using these results we provide improved distributed nameindependent routing schemes ..."
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Cited by 16 (4 self)
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independent routing scheme with a stretch of O(r 2) and tables of size 2 O(r) r! log 4 n bits; (3) a randomized algorithm that partitions the graph such that each cluster has strongdiameter O(r6 r ρ) and the probability an edge (u, v) is cut is O(r d(u, v)/ρ).
Results 1  10
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25