Disjoint Covers in Replicated Heterogeneous Arrays

Disjoint Covers in Replicated Heterogeneous Arrays

Reconfigurable chips are fabricated with redundant elements that can be used to replace the faulty elements. The fault cover problem consists of finding an assignment of redundant elements to the faulty elements such that all of the faults are repaired. In reconfigurable chips that consist of arrays of elements, redundant elements are configured as spare rows and spare columns. This paper consi...

Vertex covers by edge disjoint

Let H be a simple graph having no isolated vertices. An (H; k)-vertex-cover of a simple graph G = (V;E) is a collection H1; : : : ;Hr of subgraphs of G satisfying 1. Hi = H; for all i = 1; : : : ; r; 2. [i=1V (Hi) = V , 3. E(Hi) \ E(Hj) = ;; for all i 6= j; and 4. each v 2 V is in at most k of the Hi. We consider the existence of such vertex covers when H is a complete graph, Kt; t 3, in the co...

Paired many-to-many disjoint path covers in faulty hypercubes

A paired many-to-many k-disjoint path cover (k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all the vertices of the graph. Extending the notion of DPC, we define a paired many-to-many bipartite k-DPC of a bipartite graph G to be a set of k disjoint paths joining k distinct source-sink pairs that altogether cover the same number of vertic...

Many-to-Many Disjoint Path Covers in Double Loop Networks

Algorithms for finding disjoint path covers in unit interval graphs

A many-to-many k-disjoint path cover (k-DPC for short) of a graph G joining the pairwise disjoint vertex sets S and T , each of size k, is a collection of k vertex-disjoint paths between S and T , which altogether cover every vertex of G. This is classified as paired, if each vertex of S must be joined to a specific vertex of T , or unpaired, if there is no such constraint. In this paper, we de...