We propose an approximate algorithm for finding the maximum-weight independent set of a given graph of n nodes with associated weights. It combines three different heuristics, and its running time is O(n2) in the practice. We also propose a set of random graphs for testing and comparing the maximumweight independent set algorithms. This graphs are easy to identically generate on any computer ca...

Maximum independent set from a given set D of unit disks intersecting a horizontal line can be solved in O(n) time and O(n) space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set problem on unit disk graph which takes both time and space of O(n). The best known factor 2 approximation algorithm for this problem runs in O(n logn) time and takes O(n) sp...

The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum we...

A maximum weighted independent set of a permutation graph is a maximum subset of noncrossing chords in a matching diagram (i.e., a set of chords with end-points on two horizontal lines). The problem of nding, among all noncrossing subsets of with density at most k, one with maximum size is considered, where the density of a subset is the maximum number of chords crossing a vertical line and k i...

Satisfaction. Given a relation R between graph functions we say that a graph G satisfies R if plugging G into each function gives a true statement (e.g. G satisfies χ ≥ ∆ means χ(G) ≥ ∆(G)). We prove the following general lemma and apply it to Reed’s conjecture. The Main Lemma. If G is a graph satisfying ω ≥ 3 4 (∆ + 1), then G has an independent set I such that ω(G− I) < ω(G). In [9], Reed con...

This paper addresses the following optimization problem in a plane multihop wireless networks under the physical interference model: From a given a set of communication links whose senders transmit at a fixed uniform power level, select a maximum set of independent links. This problem is known to be NP-hard. The existing approximation algorithms which were claimed to have constant approximation...

|The results obtained from the application of a genetic algorithm, GENEsYs, to the NP-complete maximum independent set problem are reported in this work. In contrast to many other genetic algorithm based approaches that use domain-speciic knowledge, the approach presented here relies on a graded penalty term component of the tness function to penalize infeasible solutions. The method is applied...

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph’s independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph an...

The problem of finding a maximum weighted independent set (MWIS) is a classical combinatorial optimization problem of graph theory, which has been proved to be NP-complete (NPC). A 2-D DNA tile self-assembly model for solving the problem has been proposed previously, but it still has many deficiencies. In this paper, we will propose a 3-D DNA tile self-assembly model based on 2D DNA tile self-a...

A method that utilizes the polynomially solvable critical independent set problem for solving the maximum independent set problem on graphs with a nonempty critical independent set is developed. The effectiveness of the proposed approach on large graphs with large independence number is demonstrated through extensive numerical experiments.