Priority Algorithms with Advice for Disjoint Path Allocation Problems

We analyze the Disjoint Path Allocation problem (DPA) in the priority framework. Motivated by the problem of traffic regulation in communication networks, DPA consists of allocating edge-disjoint paths in a graph. While online algorithms for DPA have been thoroughly studied in the past, we extend the analysis of this optimization problem by considering the more powerful class of priority algorithms. Like an online algorithm, a priority algorithm receives its input only sequentially and must output irrevocable decisions for individual input items before having seen the input in its entirety. However, in contrast to the online setting, a priority algorithm may choose an order on the set of all possible input items and the actual input is then presented according to this order. A priority algorithm is a natural model for the intuitively well-understood concept of a greedy algorithm. Apart from analyzing the classical priority setting, we also consider priority algorithms with advice. Originally conceived to study online algorithms from an information-theoretic point of view, the concept of advice has recently been extended to the priority framework. We mainly analyze three variants of the DPA problem: The classical variant on the graph class of paths, the related problem of Length-Weighted DPA, and finally, DPA on the graph class of trees.