Optimal Scheduling of Contract Algorithms for Anytime Problem-Solving

This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a mobile searcher that must locate a hidden target in an environment that consists of a set of unbounded, concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. Both types of problems capture fundamental aspects of resource allocation under uncertainty. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems, we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using the same underlying approach.

Section: Scheduling Of Contract Algorithmsmentioning

confidence: 99%

Section: Scheduling Of Contract Algorithmsmentioning

confidence: 99%

Further connections between contract-scheduling and ray-searching problems

Angelopoulos

2021

“…We follow the notation of Bernstein et al (Bernstein, Finkelstein, and Zilberstein 2003) and Lopez-Ortiz et al (Lopez-Ortiz, Angelopoulos, and Hamel 2006). Let P denote a set of n problems.…”

Section: Preliminariesmentioning

confidence: 99%

“…For the most general case, namely solving many problems using many processors, Bernstein et al(Bernstein, Finkelstein, and Zilberstein 2003) showed an optimal simulation under the restrictive, but natural assumption that the schedule has a cyclic format. In subsequent work, López-Ortiz et al (Lopez-Ortiz, Angelopoulos, and Hamel 2006) removed the assumption of cyclicality, and showed that the schedule of (Bernstein, Finkelstein, and Zilberstein 2003) is optimal among all possible schedules. The acceleration ratio of the optimal schedule is a function of n and m, and is equal to (1 + n m )(1 + m n ) n m .…”

Section: Introductionmentioning

confidence: 99%

Optimal scheduling of contract algorithms with soft deadlines

Angelopoulos¹,

López-Ortíz²,

Hamel³

2016

A contract algorithm is an algorithm which is given, as part of its input, a specified amount of allowable computation time. In contrast, interruptible algorithms may be interrupted throughout their execution, at which point they must report their current solution. Simulating interruptible algorithms by means of schedules of executions of contract algorithms in parallel processors is a wellstudied problem with significant applications in AI. In the classical case, the interruptions are hard deadlines in which a solution must be reported immediately at the time the interruption occurs. In this paper we study the more general setting of scheduling contract algorithms at the presence of soft deadlines. This is motivated by the observation of practitioners that soft deadlines are as common an occurrence as hard deadlines, if not more common. In our setting, at the time t of interruption the algorithm is given an additional window of time w(t) ≤ c · t to continue the contract or, indeed, start a new contract (for some fixed constant c). We explore this variation using the acceleration ratio, which is the canonical measure of performance for these schedules, and derive schedules of optimal acceleration ratio for all functions w.

“…The latter is a somewhat restricted, but still very rich and intuitive class of schedules with round-robin characteristics. This restriction was removed by López-Ortiz et al [14], who showed that this acceleration ratio is indeed optimal among all possible schedules. Angelopoulos et al [3] studied the setting in which the interruptions are not absolute deadlines, but instead an additional window of computational time may be provided.…”

Section: Introductionmentioning

confidence: 99%

Interruptible algorithms for multiproblem solving

Angelopoulos

López-Ortíz

2020

In this paper we address the problem of designing an interruptible system in a setting in which n problem instances, all equally important, must be solved concurrently. The system involves scheduling executions of contract algorithms (which offer a trade-off between allowable computation time and quality of the solution) in m identical parallel processors. When an interruption occurs, the system must report a solution to each of the n problem instances. The quality of this output is then compared to the best-possible algorithm that has foreknowledge of the interruption time and must, likewise, produce solutions to all n problem instances. This extends the well-studied setting in which only one problem instance is queried at interruption time.In this work we first introduce new measures for evaluating the performance of interruptible systems in this setting. In particular, we propose the deficiency of a schedule as a performance measure that meets the requirements of the problem at hand. We then present a schedule whose performance we prove that is within a small factor from optimal in the general, multiprocessor setting. We also show several lower bounds on the deficiency of schedules on a single processor. More precisely, we prove a general lower bound of (n + 1)/n, an improved lower bound for the two-problem setting (n = 2), and a tight lower bound for the class of round-robin schedules. Our techniques can also yield a simpler, alternative proof of the main result of Bernstein et al. [4] concerning the performance of cyclic schedules in multiprocessor environments.