Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is de ned on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4 d 2k= p 3 e ) time where n denotes the number of vertices. We also propose a (1 1=r)-approxi...

We propose a heuristic for solving the maximum independent set problem for a set of processors in a network with arbitrary topology. We assume an asynchronous model of computation and we use modified Hopfield neural networks to find high quality solutions. We analyze the algorithm in terms of the number of rounds necessary to find admissible solutions both in the worst case (theoretical analysi...

The maximum weight independent set problem (MWISP) is one of the most well-known and wellstudied problems in combinatorial optimization. This paper presents a novel approach to solve MWISP exactly by decomposing the original graph into vertex-induced sub-graphs. The approach solves MWISP for the original graph by solving MWISP on the sub-graphs in order to generate columns for a branch-and-pric...

We describe three combinatorial branch-and-bound solvers for the maximum weight independent set problem. All use weighted clique covers to generate upper bounds, and all branch according to the method of Balas and Yu (1986). One extends and speeds up the method of Babel (1994). A second one employs a modified method from Balas and Yu (1986) to produce clique covers that share structural similar...

Space efficient algorithms for the maximum independent set problem for interval graphs and trees are presented in this paper. For a given set of n intervals on a real line, we can compute the maximum independent set in O( 2 s + n log s) time using O(s) extra-space. The lower bound of the time × space product for this problem is Ω(n2− ), where = O(1/ √ log n). We also propose an (1+ 1 ) approxim...

Given a graph G = (V,E), the Maximum Independent Set problem (MIS) aims to determine a subset S ⊆ V of maximum cardinality such that no two vertices of S are adjacent. This paper presents a general Swap-Based Tabu Search (SBTS) for solving the MIS. SBTS integrates distinguished features including a general and unified (k, 1)-swap operator, four constrained neighborhoods and specific rules for n...

In this paper, Radio Frequency IDentification (RFID) tag set cardinality estimation problem is considered under the model of multiple independent reader sessions with unreliable radio communication links in which transmission errors might occur. After the R-th reader session, the number of tags detected in j (j = 1, 2, ..., R) reader sessions is updated, which we call observed evidence. Then, i...

We present an output sensitive algorithm for computing a maximum independent set of an unweighted circle graph. Our algorithm requires O(nmin{d, α}) time at worst, for an n vertex circle graph where α is the independence number of the circle graph and d is its density. Previous algorithms for this problem required Θ(nd) time at worst.

Let Ind(G) be the family of all independent sets of graph G and (G) be the cardinality of an independent set of maximum size, while the set core(G) is the intersection of all maximum independent sets. An independent set A is called critical if jAj jN(A)j = maxfjSj jN(S)j : S 2 Ind(G)g. Let (G) be the size of a maximum matching, and def(G) = jV (G)j 2 (G) be the de…ciency of G. Our main …nding i...

The ordering of variables can have a significant effect on the size of the reduced binary decision diagram (BDD) that represents the set of solutions to a combinatorial optimization problem. It also influences the quality of the objective function bound provided by a limited-width relaxation of the BDD. We investigate these effects for the maximum independent set problem. By identifying variabl...