A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The proposed algorithm does not require the number of clusters in advance, and it will be determined by the ...

In this final chapter on flows, we consider a significant generalization of the maximumflow problem that (as far as we know) cannot be solved by modifying the graph and applying a standard flow algorithm. The input to our problem consists of a flow network without special source and target vertices, where each edge e has a cost $(e), in addition to the usual edge capacities and vertex balances....

A path from a source vertex v to a target vertex u is said to be a shortest path if its total cost is minimum among all v-to-u paths. Dijkstra’s algorithm is a classic shortest path algorithm, which is described in many textbooks. To justify its correctness (whose rigorous proof will be given in the next article), it is necessary to clarify its underlying principle. For this purpose, the articl...

In this paper, a fuzzy random minimum cost flow problem is presented. In this problem, cost parameters and decision variables are fuzzy random variables and fuzzy numbers respectively. The object of the problem is to find optimal flows of a capacitated network. Then, two algorithms are developed to solve the problem based on Er-expected value of fuzzy random variables and chance-constrained pro...

Let P be a simple polyhedron, possibly non-convex, whose boundary is composed of n triangular faces, and in which each face has an associated positive weight. The cost of travel through each face is the distance traveled multiplied by the face's weight. We present an-approximation algorithm for computing a weighted shortest path on P, i.e. the ratio of the length of the computed path with respe...

In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph D = (V,A) and a set K of directed commodities, an USPR is a set of flow paths Φ(s,t), (s, t) ∈ K, such that there exists a metric λ = (λa) ∈ Z+ with respect to which each Φ(s,t) is the unique shortest ...

We consider an extension of the popular matching problem in this paper. The input to the popular matching problem is a bipartite graph G = (A ∪ B, E), where A is a set of people, B is a set of items, and each person a ∈ A ranks a subset of items in an order of preference, with ties allowed. The popular matching problem seeks to compute a matching M∗ between people and items such that there is n...

In this paper, we analyze the cost allocation problem when a group of agents or nodes have to be connected to a source, and where the cost matrix describing the cost of connecting each pair of agents is not necessarily symmetric, thus extending the well-studied problem of minimum cost spanning tree games, where the costs are assumed to be symmetric. The focus is on rules which satisfy axioms re...

Reliable source to sink communication is the most important factor for an efficient routing protocol especially in domains of military, healthcare and disaster recovery applications. We present weighted energy aware multipath reliable routing (WEAMR), a novel energy aware multipath routing protocol which utilizes hotline-assisted routing to meet such requirements for mission critical applicatio...