Optimal scheduling of contract algorithms with soft deadlines

Abstract

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.

Further connections between contract-scheduling and ray-searching problems

“…Optimal schedules for the multi-instance, multi-processor setting, without restrictions, were established in López-Ortiz et al (2014). Angelopoulos et al (2008) studied contract scheduling in the presence of soft deadlines, and Angelopoulos and López-Ortiz ( 2009) introduced performance measures alternative to the acceleration ratio. In very recent work, Angelopoulos and Jin (2019) studied the setting in which a problem instance is deemed completed if the schedule has executed a contract of at least a pre-specified length, which models an end guarantee on the contract.…”

“…López-Ortiz et al (2014),Angelopoulos et al (2008)). In particular, for n problem instances, the exponential strategy with base b = n+1 n attains the optimal acceleration ratioZilberstein et al (2003) …”

Competitive Sequencing with Noisy Advice

“…Beyond these simple settings, some of the above problems, and most notably contract scheduling, have been studied under more complex settings, for which optimizing the corresponding performance measure becomes much more challenging. This includes settings in which one must schedule executions of the contract algorithm for several problem instances, as well as the setting in which the executions can be scheduled in several parallel processors, see, e.g., [12,35,11,24,7,6,4,21]. All these works show theoretical upper and lower bounds on the performance of the corresponding schedules.…”

“…To achieve this result, we introduce a new application of Gal's functional theorem [19]. This is the main tool for showing lower bounds in search theory but also in contract scheduling: see, e.g., Chapters 7 and 9 in [1] and [25,32], for its applications in search theory, as well as [24,7,6,4] for its applications in contract scheduling. Note that all previous work has applied this theorem in a "black-box" manner: specifically, a typical application of this theorem gives a lower bound to the performance of the algorithms, as a function of a parameter α X , that depends on the sequence X (see Theorem 11 for details); say that f (α X ) is this lower bound expression.…”

Interruptible algorithms for multiproblem solving

“…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.…”