Contract Algorithms and Robots on Rays: Unifying Two Scheduling Problems

We study two apparently different, but formally similar, scheduling problems. The first problem involves contract algorithms, which can trade off run time for solution quality, as long as the amount of available run time is known in advance. The problem is to schedule contract algorithms to run on parallel processors, under the condition that an interruption can occur at any time, and upon interruption a solution to any one of a number of problems can be requested. Schedules are compared in terms of acceleration ratio, which is a worst-case measure of efficiency. We provide a schedule and prove its optimality among a particular class of schedules. Our second problem involves multiple robots searching for a goal on one of multiple rays. Search strategics are compared in terms of time-competitive ratio, the ratio of the total search time to the time it would take for one robot to traverse directly to the goal. We demonstrate that search strategies and contract schedules are formally equivalent. In addition, for our class of schedules, we derive a formula relating the acceleration ratio of a schedule to the time-competitive ratio of the corresponding search strategy.