Interference-aware scheduling for wireless communications is crucial to improve the network throughput. In this paper, we study the problem of Maximum Weighted Independent Set of Links (MWISL) under the physical interference model in wireless networks. Given a set of communication links distributed in a two-dimensional Euclidean plane, assume each link is associated with a positive weight which...

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized sparse graphs, as well as high-quality independent sets in huge sparse graphs that are intractable for exact (exponential-time) algorithms. However, a major dra...

Several algorithms are presented. The standard algorithm generates all N anticliques of a graph with v vertices in time O(Nv). It can be adapted to e.g. generate all maximum cardinality anticliques, or just one maximum anticlique. The latter is our main achievement and was programmed using the Mathematica 6.0 code. For a random (45, 92)-graph G a maximum anticlique of size 21 was found in 1.344...

The Maximum Independent Set problem is NP-hard and remains NP-hard for graphs with maximum degree three (also called subcubic graphs). In our talk we will study its complexity in hereditary subclasses of subcubic graphs. Let A r q be the graph consisting of an induced cycle C q and an induced path with r edges having an endvertex in common with the C q , where A 1 4 is known as the banner. Our ...

We develop an experimental algorithm of exact solving for the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set contains more elements than preceding one. For this purpose, we use a technique, developed by Ford and Fulkerson for the finite partially ordered sets, in particular,...

The independent set on a graph G = (V, E) is a subset of V such that no two vertices in the subset have an edge between them. The maximum independent set problem on G seeks to identify an independent set with maximum cardinality, i.e. maximum independent set or MIS. The maximum independent set problem on a general graph is known to be NP-complete. On certain classes of graphs MIS can be compute...

As an easy example of divide, prune, and conquer, we give an output-sensitive O(n log k)-time algorithm to compute, for n intervals, a maximum independent set of size k.

We present a simple algorithm for the maximum independent set problem in an n-vertex graph with degree bounded by 4, which runs in O∗(1.1455n) time and improves all previous algorithms for this problem. In this paper, we use the “Measure and Conquer method” to analyze the running time bound, and use some good reduction and branching rules with a new idea on setting weights to obtain the improve...

Given a graph G = (V, E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. We present a fast local search routine for this problem. Our algorithm can determine in linear time if a maximal solution can be improved by replacing a single vertex with two others. We also show that an incremental version of this method can...

Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can nd an O(logn)-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit height, we can nd a 2-approximation in O...