The independence number of a graph G, denoted by α(G), is the cardinality of an independent set of maximum size in G, while μ(G) is the size of a maximum matching in G, i.e., its matching number. G is a König–Egerváry graph if its order equals α(G)+μ(G). In this paper we give a new characterization of König–Egerváry graphs. We also deduce some properties of vertices belonging to all maximum ind...

Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GREEDYMATCHING. In wide contrast to the maximum weight matching problem, for which many efficient algorithms are known, we prove that GREEDYMATCHING is strongly NP-hard and A...

We consider the problem of estimating the weight of a maximum weighted matching of a weighted graph G(V, E) whose edges are revealed in a streaming fashion. We develop a reduction from the maximum weighted matching problem to the maximum cardinality matching problem that only doubles the approximation factor of a streaming algorithm developed for the maximum cardinality matching problem. Our re...

Recently there has been extensive work on maintaining (approximate) maximum matchings in dynamic graphs. We consider a generalisation of this problem known as themaximum b-matching: Every node v has a positive integral capacity bv, and the goal is to maintain an (approximate) maximum-cardinality subset of edges that contains at most bv edges incident on every node v. The maximum matching proble...

When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which c...

Preemptive online algorithms for the maximum matching problem maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The...

Let H = (V, E) be a hypergraph and let k ≥ 1 and l ≥ 0 be fixed integers. LetM be the matroid with ground-set E s.t. a set F ⊆ E is independent if and only if each X ⊆ V with k|X| − l ≥ 0 spans at most k|X| − l hyperedges of F . We prove that if H is dense enough, thenM satisfies the double circuit property, thus the min-max formula of Dress and Lovász on the maximum matroid matching holds forM...

Given a preference system (G, ≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G, ≺) with maximum total weight. We study this N P-hard problem using linear programming and polyhedral approaches, and show that the Rothblum system for defining the fractional stable matching poly...

In this paper we introduce the incremental assignment problem. In this problem, a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known, and the maximum weighted matching of the extended graph is sought. We propose an O(|V |2) algorithm for the problem.

This paper presents a suitable and quick way to choose earthquake records in non-linear dynamic analysis using optimization methods. In addition, these earthquake records are scaled. Therefore, structural responses of three different soil-frame models were examined, the change in maximum displacement of roof was analyzed and the damage index of whole structures was measured. The soil classifica...