Advice complexity of disjoint path allocation

Abstract

This paper contributes to the research of advice complexity of online problems. Namely, we discuss the disjoint path allocation problem in various versions, based on the choice of values of the calls, and ability to preempt. The advice complexity is measured relative to either the length of the input sequence of requests, or the length of the input path. We provide lower and upper bounds on advice complexity of optimal online algorithms for these problems, and some bounds on trade-off between competitiveness and advice complexity. One of the results is an improved lower bound of n − 1 on advice complexity for the non-preemptive version with constant values of calls. For all considered variations, the newly provided lower and upper bounds on advice complexity of optimal algorithms are linear, and therefore asymptotically tight.