Small Maximal Independent Sets and Faster Exact Graph Coloring
نویسنده
چکیده
We show that, for any n-vertex graph G and integer parameter k, there are at most 34k−n4n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(34k−n4n−3k). These bounds are tight when n/4 ≤ k ≤ n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3/4)) ≈ 2.4150, improving a previous O((1 + 3)) ≈ 2.4422 algorithm of Lawler (1976).
منابع مشابه
Maximal Independent Set Based Approach for Graph Coloring Problem
Graph coloring problem is a well-known NP-complete problem and there are many approaches proposed to solve this problem. For a graph coloring algorithm to be efficient, it must color the input graph with minimum colors and must also find the solution in the minimum possible time. Heuristic approaches emphasize on the time complexity while the exact approaches concentrate on the number of colors...
متن کاملMAXIMAL INDEPENDENT SETS FOR THE PIXEL EXPANSION OF GRAPH ACCESS STRUCTURE
Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...
متن کاملMaximal Independent Sets for the Pixel Expansion of Graph Access Structure
Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was ...
متن کاملParallel Jobs Scheduling with a Specific Due Date: Asemi-definite Relaxation-based Algorithm
This paper considers a different version of the parallel machines scheduling problem in which the parallel jobs simultaneously requirea pre-specifiedjob-dependent number of machines when being processed.This relaxation departs from one of the classic scheduling assumptions. While the analytical conditions can be easily statedfor some simple models, a graph model approach is required when confli...
متن کاملExact Graph Coloring Algorithms of Getting Partial and All Best Solutions
Designing effective exact algorithms for graph coloring problem is still an interesting topic. Instead of getting only one best solution, two exact graph coloring algorithms, PexaCol (Partial best solutions Exact graph Coloring algorithm) and AexaCol (All best solutions Exact graph Coloring algorithm), have been proposed, which are able to obtain a best solution subset and all best solutions re...
متن کامل