We propose algorithms for a special type of geometric facility location problem in which customers may choose not to use the facility. We minimize the maximum cost incurred by a customer, where the cost itself is a minimum between two costs, according to whether the facility is used or not. We therefore call this type of location problem a min-max-min geometric facility location problem. As a f...

Abstract The Linear Complementarity Problem ) , ( q M LCP is to find a vector x in n IR satisfying 0  x , 0   q Mx and x T (Mx+q)=0, where M as a matrix and q as a vector, are given data. In this paper we show that the linear complementarity problem is completely equivalent to finding the fixed point of the map x = max (0, (I-M)x-q); to find an approximation solution to the second problem, w...

We give a simple deterministic O(logK/ log logK) approximation algorithm for the Min-Max Selecting Items problem, where K is the number of scenarios. While our main goal is simplicity, this result also improves over the previous best approximation ratio of O(logK) due to Kasperski, Kurpisz, and Zieliński (Information Processing Letters (2013)). Despite using the method of pessimistic estimators...

This paper deals with fuzzy transshipment problem in which available commodity frequently moves from one source to another source before reaching its actual destination. Here Max – Min method is introduced to find initial feasible solution for the large scale fuzzy transshipment problem. Mathematics Subject Classification: 03E72

Let G be a graph with the vertex set V (G), edge set E(G). A vertex labeling is a bijection f : V (G)→ {1, 2, . . . , |V (G)|}. The weight of e = uv ∈ E(G) is given by g(e) = min{f(u), f(v)}. The min-sum vertex cover (msvc) is a vertex labeling that minimizes the vertex cover number μs(G) = ∑ e∈E(G) g(e). The minimum such sum is called the msvc cost. In this paper, we give both general bounds a...

We are concerned with an algorithm for determining p which is more efficient than the obvious one of generating the n\ possible assignments then straightforwardly selecting p. A method for demonstrating an assignment containing p. is also of concern, but such a method is easily evolved using the tools necessary to determine p. Before proceeding we define a nonzero column of a set of r rows of A...

Consider a binary matroid M given by its matrix representation. We show that if M is a lift of a graphic or a cographic matroid, then in polynomial time we can either solve the single commodity flow problem for M or find an obstruction for which the Max-Flow MinCut relation does not hold. The key tool is an algorithmic version of Lehman’s Theorem for the set covering polyhedron.

Given a network G = (V,E), we say that a subset of vertices S ⊆ V has radius r if it is spanned by a tree of depth r. We are interested in determining whether G has a cutset that can be written as the union of k sets of radius r. This generalizes the notion of k-vertex connectivity, since in the special case r = 0, a set spanned by a tree of depth r is a single vertex. Our motivation for consid...

Let G = (V, E) be a graph with positive edge weights and let V’ c V. The min VI-cut prohlenl is to find a minimum weight set E’ E E such that no two nodes of V’ occur in the same component of G’ = (V, E\E’). Our main results are two new structural theorems for optimal solutions to the min V-cut problem when G is planar. The first theorem establishes for the first time a close connection between...