Existing work that schedules concurrent transmissions collision-free suffers from low channel utilization. We propose the Optimal Node Activation Multiple Access (ONAMA) protocol to achieve maximal channel spatial reuse through a distributed maximal independent set (DMIS) algorithm. To overcome DMIS’s excessive delay in finding a maximal independent set, we devise a novel technique called pipel...

In this paper we study the question of existence of a cycle basis (that is, a basis consisting only of cycles) for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then the set of fundamental circuits of any maximal independent set of M can be completed to a cycle basis of Z(M); moreover, for any one-element extension M 0 of such matroid...

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...

Cycle bases for lattices of binary matroids with no Fano dual minor and their one-element extensions Abstract In this paper we study the question of existence of a cycle basis (that is, a basis consisting only of cycles) for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then the set of fundamental circuits of any maximal independent s...

A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence polynomial of G to be S(G, z) = ∑ skz k. This paper develops a new graph theoretic operation called power magnification that preserves well-coveredness and has the effect of multiplying an independence polynomial by zc wh...

A quasi-hamiltonian path in a semicomplete multipartite digraph D is a path which visits each maximal independent set (also called a partite set) of D at least once. This is a generalization of a hamiltonian path in a tournament. In this paper we investigate the complexity of finding a quasi-hamiltonian path, in a given semicomplete multipartite digraph, from a prescribed vertex x to a prescrib...

In [8] an algorithm has been presented that computes a maximal independent set (MIS) withinO(log n/F + log n polyloglogn) rounds in an n-node multichannel radio network with F commu-nication channels. The paper uses a multichannel variant of the standard graph-based radio networkmodel without collision detection and it assumes that the network graph is a polynomially bounded in-...

People arrive one at a time to a theater consisting of m rows of length n. Being unfriendly they choose seats at random so that no one is in front of them, behind them or to either side. What is the expected number of people in the theater when it becomes full, i.e., it cannot accommodate any more unfriendly people? This is equivalent to the random process of generating a maximal independent se...

Generating all configurations that satisfy a given specification is a well-studied problem in Combinatorics and in Graph theory suggesting many interesting problems. Among them, generating all maximal independent sets of a given graph is one that has attracted considerable attention [3,4,7]. A maximal independent set of a graph G = (V,E) is a subset V ′ ⊆ V such that no two vertices in V ′ are ...

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input graph G without cycles of length 4, 5, and 6, we cha...