Oscar Garrido

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Let k be a positive integer, a subset Q of the set of vertices of a graph G is k-dependent in G if each vertex of Q has no more than k neighbours in Q. We present a parallel algorithm which computes a maximal k-dependent set in a graph on n nodes in time O(log 4 n) on an EREW PRAM with O(n 2) processors. In this way, we establish the membership of the(More)
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(More)
Graphs are the most widely used of all mathematical structures. There is uncountable number of interesting computational problems de ned in terms of graphs. A graph can be seen as a collection of vertices (V ), and a collection of edges (E) joining all or some of the vertices. One is very often interested in nding subsets, either from the set V of vertices(More)
We present a randomized NC solution to the problem of constructing a maximum (cardinality) f-matching. As a corollary, we obtain a randomized NC algorithm for the problem of constructing a graph satisfying a sequence d 1 ; d 2 ;...; d n of equality degree constraints. We provide an optimal NC algorithm for the decision version of the degree sequence problem(More)
When is a sequence of integers realizable as the degree sequence of a graph? There are well known necessary and suucient conditions for a sequence of integers to constitute degrees of a graph 1]. There exists a sequential linear time algorithm that construct a graph from a given degree sequence. This algorithm however seems to be inherenty sequencial, and(More)
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