A stochastic matching model on hypergraphs

Stochastic Matching in Hypergraphs

We study the stochastic matching problem on k-uniform hypergraphs. In this problem, we are given a hypergraphH on V vertices. With each hyperedge E, we are given a probability pe of its existence i.e. an edge e exists in the hypergraph with probability pe , independent of all other edges. Each edge also has a weight associated with it. Our goal is to construct a matching with maximum expected w...

Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model

This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of interactions with a structure of hypergraph. This new perspective is more appropriate to define stochastic spatial processes in which large blocks of vertices may ...

On the matching polynomial of hypergraphs∗

The concept of the matching polynomial of a graph, introduced by Farrell in 1979, has received considerable attention and research. In this paper, we generalize this concept and introduce the matching polynomial of hypergraphs. A recurrence relation of the matching polynomial of a hypergraph is obtained. The exact matching polynomials of some special hypergraphs are given. Further, we discuss t...

A Stochastic Optimization Model for Groundwater Management

A Stochastic Model for Water Resources Management

Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. Over the past decades, controversial and conflictladen water-allocation issues among competing municipal, industrial and agricultural interests have raised increasing concerns. Particularly, growing population, varying natural conditions and shrinking wa...