Color-coding algorithms to the balanced path problem: computational issues

Cappanera, Paola and Scutellà, Maria Grazia (2007) Color-coding algorithms to the balanced path problem: computational issues. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

Given a weighted directed network G, we consider the problem of computing k balanced paths from given source nodes to given destination nodes of G, i.e., k paths such that the difference in cost between the longest and the shortest path is minimized. Although not yet investigated by the OR scientific community, except for some preliminary theoretical results concerning the special case of acyclic networks, balanced path problems arise in several interesting applications, both in transportation and in telecommunication settings. For example, in load balancing of multiple Quality of Service (QoS) paths in the IP Telephony service, the problem of minimizing the end-to-end delay difference between the longest and the shortest path in multiple path management schemes has been suggested in the literature as a promising line of research. In this work the focus is on the computation of node-disjoint balanced paths in the general case, where the input graph G may have any structure. Starting from some algorithmic ideas proposed for acyclic networks, a general framework is firstly described, which is based on the color-coding method for computing simple paths. Then the general framework is specialized and a pool of algorithms is designed which includes both an exact approach as well as alternative heuristics. The algorithms have been tested on a large suite of instances generated from some benchmark telecommunication instances. The obtained computational results are very interesting: in some cases, the exact color-coding algorithm produces the optimal solution very rapidly; in the remaining cases, some of the proposed heuristics are able to generate high quality solutions in a very quick time.

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