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A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of the integers assigned to its ends. For many application one hopes to find an LA with small cost. However, it is a… (More)
For digraphs G and H, a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f (u)f (v) ∈ A(H). If, moreover , each vertex u ∈ V (G) is associated with costs c i (u), i ∈ V (H), then the cost of a homomorphism f is u∈V (G) c f (u) (u). For each fixed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), can be… (More)
We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph H = (B, S). Vertices in B are thought of as goods or services that must be bought to produce items in S that are to be sold. An edge from j ∈ S to i ∈ B indicates that the… (More)
We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each gride cell is 1 × 1. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from… (More)
We conjecture new sufficient conditions for a digraph to have a Hamilton cycle. In view of applications, the conjecture is of interest in the areas where unitary matrices are of importance including quantum mechanics and quantum computing.