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To practically solve NP-hard combinatorial optimization problems , local search algorithms and their parallel implementations on PVM or MPI have been frequently discussed. Since a huge number of neighbors may be examined to discover a locally optimal neighbor in each of local search calls, many of parallelization schemes, excluding so-called the multi-start… (More)

Given a simple, undirected graph G = (V , E) and a weight function w : E → Z + , we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. It has previously been shown that the unweighted version of the problem is solvable in polynomial time while the weighted version is (weakly) NP-hard. In… (More)

In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics and a collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network… (More)

An L(2, 1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that | f (x) − f (y)| ≥ 2 if x and y are adjacent and | f (x) − f (y)| ≥ 1 if x and y are at distance 2 for all x and y in V(G). A k-L(2, 1)-labeling is an assignment f : V(G) → {0,. .. , k}, and the L(2, 1)-labeling problem asks the minimum… (More)

Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving… (More)

In a coalescing random walk, a set of particles make independent discrete-time random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues a random walk through the graph. Let G = (V, E), be an undirected and connected graph, with n vertices and m edges. The coalescence time, C(n), is… (More)

We study the problem of orienting the edges of a weighted graph such that the maximum weighted out-degree of vertices is minimized. This problem, which has applications in the guard arrangement for example , can be shown to be N P-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following… (More)