Greedy graph matching provides us with a fast way to coarsen a graph during graph partitioning. Direct algorithms on the CPU which perform such greedy matchings are simple and fast, but offer few handholds for parallelisation. To remedy this, we introduce a fine-grained shared-memory parallel algorithm for maximal greedy matching, together with an implementation on the GPU, which is faster (spe...

We show how to extend the RNC-algorithm for maximal match-ings due to Israeli-Itai (presented in 5]) to compute maximal (with respect to set of edges inclusion) f-matchings. Our algorithm works in O(log 2 n) time on an arbitrary Crcw Pram with a linear number of processors. Also we slightly improve a constant coeecient in the analysis of the Israeli-Itai algorithm. Finally we present more eecie...

Yannakakis and Gavril showed in [10] that the problem of finding a maximal matching of minimum size (MMM for short), also called Minimum Edge Dominating Set, is NP-hard in bipartite graphs of maximum degree 3 or planar graphs of maximum degree 3. Horton and Kilakos extended this result to planar bipartite graphs and planar cubic graphs [6]. Here, we extend the result of Yannakakis and Gavril in...

Given an undirected graph, the problem of finding a maximal matching that has minimum total weight is NP-hard. This problem has been studied extensively from a graph theoretical point of view. Most of the existing literature considers the problem in some restricted classes of graphs and give polynomial time exact or approximation algorithms. On the contrary, we consider the problem on general g...

We study the algorithm that iteratively removes adjacent vertices from a simple, undirected graph until no edge remains. This algorithm is a well-known 2-approximation to three classical NP-hard optimization problems: MINIMUM VERTEX COVER, MINIMUM MAXIMAL MATCHING and MINIMUM EDGE DOMINATING SET. We show that the worst-case approximation factor of this simple method can be expressed in a finer ...

We investigate the problem of finding a maximal matching that has minimum total weight on a given edge-weighted graph. Although the minimum weight maximal matching problem is NP-hard in general, polynomial time exact or approximation algorithms on several restricted graph classes are given in the literature. In this paper, we propose an exact algorithm for solving several variants of the proble...

In this paper we analyze the average queue lengths in a combined input-output queued switch using a maximal size matching scheduling algorithm. We compare these average queue lengths to the average queue lengths achieved by an optimal switch. We model the cell arrival process as independent and identically distributed between time slots and uniformly distributed among input and output ports. Fo...

We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic “approximately-maximal” fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of Bhattacharya, Henzinger, and Nanongkai (SODA 2017), we obtain a novel result for the integral problem. Specifically, our main result is a randomized fully-dynamic (...

Multiple parallel transactions in new-type distributed software environment result in that the events produced by every transaction are randomly ranked. If the tokens of these events are incomplete or unavailable, it is difficult for software system to distinguish these events to actually belong to which transaction, corresponding transaction analysis and prediction can’t be executed. In this p...

The paper aims to come up with a system that examines the degree of semantic equivalence between two sentences. At the core of the paper is the attempt to grade the similarity of two sentences by finding the maximal weighted bipartite match between the tokens of the two sentences. The tokens include single words, or multiwords in case of Named Entitites, adjectivally and numerically modified wo...