Approximating Maximum Independent Sets by Excluding Subgraphs 1
نویسنده
چکیده
An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to O(n=(logn) 2 ). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strong simultaneous performance guarantee for the clique and coloring problems. The framework of subgraph-excluding algorithms is presented. We survey the known approximation algorithms for the independent set (clique), coloring, and vertex cover problems and show how almost all t into that framework. We show that among subgraph-excluding algorithms, the ones presented achieve the optimal asymptotic performance guarantees. CR Categories: F.2.2, G.2.2
منابع مشابه
Counting Subgraphs via Homomorphisms
We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, Husfeldt and Koivisto for computing the chromatic polynomial, the classical algorithm of Kohn, Go...
متن کامل(Wireless) Scheduling, Graph Classes, and c-Colorable Subgraphs
Inductive k-independent graphs are a generalization of chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced c-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting c sets of pairwise non-conflicting jobs (modele...
متن کاملThe maximum number of complete subgraphs in a graph with given maximum degree
Extremal problems involving the enumeration of graph substructures have a long history in graph theory. For example, the number of independent sets in a d-regular graph on n vertices is at most (2 − 1) by the Kahn-Zhao theorem [7, 12]. Relaxing the regularity constraint to a minimum degree condition, Galvin [5] conjectured that, for n ≥ 2d, the number of independent sets in a graph with δ(G) ≥ ...
متن کاملAlgorithms for maximum induced multicliques and complete multipartite subgraphs in polygon-circle graphs
A graph is a multiclique if its connected components are cliques. A graph is a complete multipartite graph if its vertex set has a partition into independent sets such that every two vertices in different independent sets are adjacent. The complement of a graph G is denoted coG. A graph is a multiclique-multipartite graph if its vertex set has a partition U, W such that G(U) is complete multipa...
متن کاملExtending the Max Algorithm for maximum independent set
The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G. We present a set of forbidden induced subgraphs such that Algorithm MAX always results in finding a maximum independent set ofG. We also describe two modifications of Algorithm MAX and sets of forbidden indu...
متن کامل