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Approximation Algorithms for the MaxColoring Problem
"... Given a graph G = (V; E) and positive integral vertex weights w: V! N, the maxcoloring problem seeks to find a proper vertex coloring of G whose color classes C1; C2; : : : ; Ck, minimize ..."
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Cited by 21 (0 self)
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Given a graph G = (V; E) and positive integral vertex weights w: V! N, the maxcoloring problem seeks to find a proper vertex coloring of G whose color classes C1; C2; : : : ; Ck, minimize
Bounded MaxColorings of Graphs
, 2009
"... In a bounded maxcoloring of a vertex/edge weighted graph, each color class is of cardinality at most b and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded maxvertex/edgecoloring problems ask for such a coloring minimizing the sum of all color classes ’ weights ..."
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/3 approximation algorithm. For the bounded maxedgecoloring problem, we prove approximation factors of 3 − 2 / √ 2b, for general graphs, min{e,3 − 2 / √ b}, for bipartite graphs, and 2, for trees. Furthermore, we show that this problem is NPcomplete even for trees. This is the first complexity result for maxcoloring
Maxcoloring and online coloring with bandwidths on interval graphs
, 2008
"... Given a graph G = (V, E) and positive integral vertex weights w: V → N, the maxcoloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2,..., Ck, minimize ∑k i=1 maxv∈C w(v). This problem, restricted to interval graphs, arises whenever there is a need i to design dedic ..."
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Cited by 6 (0 self)
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and use this to devise a simple 2approximation algorithm for maxcoloring on interval graphs. We also show that a simple firstfit strategy, that is a natural choice for this problem, yields an 8approximation algorithm. We show this result by proving that the firstfit algorithm for online coloring
Buffer Minimization Using MaxColoring
, 2003
"... Given a graph G = (V, E) and positive integral vertex weights w: V → N, the maxcoloring problem seeks to find a proper vertex coloring of G whose color classes C_1, C_2, ..., C_k, minimize i=1 max v#C i w(v). This problem, restricted to interval graphs, arises whenever there is a need to d ..."
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Cited by 37 (2 self)
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Given a graph G = (V, E) and positive integral vertex weights w: V → N, the maxcoloring problem seeks to find a proper vertex coloring of G whose color classes C_1, C_2, ..., C_k, minimize i=1 max v#C i w(v). This problem, restricted to interval graphs, arises whenever there is a need
Clique Clustering yields a PTAS for maxColoring Interval Graphs
, 2011
"... We are given an interval graph G = (V,E) where each interval I ∈ V has a weight wI ∈ R +. The goal is to color the intervals V with an arbitrary number of color classes C1,C2,...,Ck such that ∑ k i=1 maxI∈Ci wI is minimized. This problem, called maxcoloring interval graphs, contains the classical p ..."
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problem of coloring interval graphs as a special case for uniform weights, and it arises in many practical scenarios such as memory management. Pemmaraju, Raman, and Varadarajan showed that maxcoloring interval graphs is NPhard (SODA’04) and presented a 2approximation algorithm. Closingagap which
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
On Powers of Chordal Graphs And Their Colorings
 Congr. Numer
, 2000
"... The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of t ..."
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Cited by 24 (1 self)
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of the known facts that any power of an interval graph is an interval graph, and that any odd power of a general chordal graph is again chordal. We then show that it is computationally hard to approximately color the even powers of n vertex chordal graphs within an n 1 2 \Gammaffl factor, for any ffl
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can
Results 1  10
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54,111