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This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) There is a polynomial-time approximation scheme for planar graphs; (2) there is a polynomial-time 3 5-approximation algorithm for graphs; (3) it is NP-hard to approximate the problem within ratio 259 260 + for graphs; (4) there is a linear-time… (More)

In this paper, we reÿne upper and lower bounds for the channel capacity of a serial, binary rewritable medium in which no consecutive locations may store 1's and no consecutive locations may be altered during a single rewriting pass. This problem was originally examined by Cohn (Discrete. Appl. Math. 56 (1995) 1) who proved that C, the channel capacity of… (More)

This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) there is a polynomial-time approximation scheme for planar unweighted graphs; (2) there is a polynomial-time algorithm with approximation ratio 3/5 for unweighted graphs; (3) it is NP-hard to approximate the problem within ratio 545/546 +… (More)

In this paper, we propose a deadlock-free routing in irregular networks using preex routing. Preex routing is a special type of routing with a compact routing table associated with each node (processor). Basically, each outgoing channel of a node is assigned a special label and an outgoing channel is selected if its label is a preex of the label of the… (More)

Role assignments, introduced by Everett and Borgatti [2], who called them role col-orings, formalize the idea, arising in the theory of social networks, that individuals of the same social role will relate in the same way to the individuals playing counterpart roles. If G is a graph, a k-role assignment is a function r mapping the vertex set onto the set of… (More)

—A shortest-path routing is optimal if it maximizes the probability of reaching the destination from a given source, assuming that each link in the system has a given failure probability. An approximation for the shortest-path routing policy, maximum-shortest-path (MSP) routing was proposed by Wu [3]. Reference [3] • shows that MSP is optimal in the mesh… (More)

—The TNM (Tumor, Lymph Node, Metas-tasis) is a widely used staging system for predicting the outcome of cancer patients. However, the TNM is not accurate in prediction, partially due to the fact of deficient staging within and between stages. Based on the availability of large cancer patient datasets, there is a need to expand the TNM. In this paper, we… (More)

A tournament Tn is an orientation of a complete graph on n vertices. A king in a tournament is a vertex from which every other vertex is reachable by a path of length at most 2. A sorted sequence of kings in a tournament Tn is an ordered list of its vertices u n−1. In particular, if Tn is transitive, searching for a sorted sequence of kings in Tn is… (More)

ÐIn [1], Libeskind-Hadas provided a tight lower bound on the number of channels required by a broad class of deadlock-free wormhole routing algorithms. In this short note, we show a simpler proof of the tight lower bound.

A king u in a tournament is a player who beats any other player v directly or indirectly. That is, either u → v (u beats v) or there exists a third player w such that u → w and w → v. A sorted sequence of kings in a tournament of n players is a sequence of players, S = The existence of a sorted sequence of kings in any tournament is shown by Lou et al.… (More)