Online Assignment Algorithms for Dynamic Bipartite Graphs

TL;DR

This paper introduces online algorithms for dynamic bipartite graph assignment problems, modeling real-time resource allocation with changing graph elements and attributes, and evaluates their competitive ratios.

Contribution

It presents primal-dual algorithms for dynamic bipartite graph assignment problems with changing edges and attributes, analyzing their competitive ratios.

Findings

Algorithms achieve competitive ratios within theoretical bounds.

Effective handling of disappearing and reappearing nodes and edges.

Framework applicable to real-time distributed resource allocation.

Abstract

This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints. The cost and constraints are functions of attributes of the edges, nodes and online service requests. Novelty of this work is that it models real-time distributed resource allocation using an approach to solve this theoretical problem. This paper studies variants of this assignment problem where the edges, producers and consumers can disappear and reappear or their attributes can change over time. Primal-Dual algorithms are used for solving these problems and their competitive ratios are evaluated.