Approximation Algorithms for Intersection Graphs

We study three complexity parameters that, for each vertex v , are an upper bound for the number of cliques that are sufficient to cover a subset S ( v ) of its neighbors. We call a graph k-perfectly groupable if S ( v ) consists of all neighbors, k-simplicial if S ( v ) consists of the neighbors wi...

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Vydáno v:	Algorithmica Ročník 68; číslo 2; s. 312 - 336
Hlavní autoři:	Kammer, Frank, Tholey, Torsten
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Boston Springer US 01.02.2014 Springer
Témata:	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Convex and discrete geometry Data Structures and Information Theory Exact sciences and technology Flows in networks. Combinatorial problems Geometry Information retrieval. Graph Mathematics Mathematics of Computing Operational research and scientific management Operational research. Management science Sciences and techniques of general use Theoretical computing Theory of Computation Parameterized approximation algorithms Graph algorithms NP-hard problems Intersection graphs Intersection Partition Tree(graph) Dominating set Similarity Graph clique Chordal graph Graph theory Approximation algorithm Polynomial time Upper bound NP hard problem Graph colouring Independent set Intersection graph Parameterized complexity
ISSN:	0178-4617, 1432-0541
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Popis
Shrnutí:	We study three complexity parameters that, for each vertex v , are an upper bound for the number of cliques that are sufficient to cover a subset S ( v ) of its neighbors. We call a graph k-perfectly groupable if S ( v ) consists of all neighbors, k-simplicial if S ( v ) consists of the neighbors with a higher number after assigning distinct numbers to all vertices, and k-perfectly orientable if S ( v ) consists of the endpoints of all outgoing edges from v for an orientation of all edges. These parameters measure in some sense how chordal-like a graph is—the last parameter was not previously considered in literature. The similarity to chordal graphs is used to construct simple polynomial-time approximation algorithms with constant approximation ratio for many NP-hard problems, when restricted to graphs for which at least one of the three complexity parameters is bounded by a constant. As applications we present approximation algorithms with constant approximation ratio for maximum weighted independent set, minimum (independent) dominating set, minimum vertex coloring, maximum weighted clique, and minimum clique partition for large classes of intersection graphs.
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-012-9671-1