Windows scheduling of arbitrary length jobs on parallel machines

Bar-Noy, Amotz; Ladner, Richard E.; Tamir, Tami; VanDeGrift, Tammy

doi:10.1145/1073970.1073980

Cited by 3 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A proof for the case where i must be granted an exact w i window is given in [Bar-Noy, Bhatia, Naor, and Schieber 2002]. Another proof that is suitable also for the flexible case in which the schedule of i need not be perfect is given in Bar-Noy, Ladner, and Tamir [2007].…”

Section: Prior Results and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A general buffer scheme for the windows scheduling problem

Bar-Noy

Ladner

Christensen

et al. 2009

ACM J. Exp. Algorithmics

Self Cite

View full text Add to dashboard Cite

Broadcasting is an efficient alternative to unicast for delivering popular on-demand media requests. Broadcasting schemes that are based on windows scheduling algorithms provide a way to satisfy all requests with both low bandwidth and low latency.Consider a system of n pages that need to be scheduled (transmitted) on identical channels an infinite number of times. Time is slotted, and it takes one time slot to transmit each page. In the windows scheduling problem (WS) each page i, 1 ≤ i ≤ n, is associated with a request window w i . In a feasible schedule for WS, page i must be scheduled at least once in any window of w i time slots. The objective function is to minimize the number of channels required to schedule all the pages.The main contribution of this paper is the design of a general buffer scheme for the windows scheduling problem such that any algorithm for WS follows this scheme. As a result, this scheme can serve as a tool to analyze and/or exhaust all possible WS-algorithms.The buffer scheme is based on modelling the system as a nondeterministic finite state machine in which any directed cycle corresponds to a legal schedule and vice-versa. Since WS is NP-hard, we present some heuristics and pruning-rules for cycle detection that ensure reasonable cycle-search time.By introducing various rules, the buffer scheme can be transformed into deterministic scheduling algorithms. We show that a simple page-selection rule for the buffer scheme provides an optimal schedule to WS for the case where all the w i 's have divisible sizes, and other good schedules for some other general cases. By using an exhaustive-search, we prove impossibility results for other important instances.

show abstract

Section: Prior Results and Related Workmentioning

confidence: 99%

“…It is known[Bar-Noy, Ladner, Tamir, and VANDEGRIFT 2005] that preemptive WS is equivalent to WS of unit-length pages. Thus, we consider here only the more restricted problem of nonpreemptive scheduling.2 We assume here that the next processing of a page cannot start during its current processing.…”

mentioning

confidence: 99%