## Optimal Scheduling of Contract Algorithms for Any-time Problems

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## Abstract

A contract algorithm is an algorithm which is given, as part of the input, a specified amount of allowable computation time. The algorithm must then compute a solution within the alloted time. An {\it interruptible} algorithm, in contrast, can be interrupted at an arbitrary point in time and must produce a solution. It is known that contract algorithms can simulate interruptible algorithms using iterative deepening techniques. This simulation is done at a penalty in the performance of the solution, as measured by the so-called acceleration ratio. In this paper we give matching (i.e. optimal) upper and lower bounds for the acceleration ratio under this simulation. This resolves an open conjecture of Bernstein et al. [IJCAI 2003] who gave an ingenious optimal schedule under the restricted setting of round robin and length-increasing processor schedules, but whose optimality in the general unrestricted case remained open.