Choosing preemption points to minimize typical running times
The problem of selecting "effective preemption points" in a program --- points in the code at which to permit preemption --- in order to minimize overall running time is considered. Prior solutions that have been proposed for this problem are based on workload models in which worst-case known upper bounds are assumed for the duration needed to perform preemptions at particular points in the code, and of the time needed to non-preemptively execute the code between preemption points. Since these solutions are based on worst-case assumptions, they tend to select effective preemption points in a conservative manner; consequently the overall execution time of the program may be needlessly large under most typical run-time circumstances. We consider a more general workload model in which "typical" values, as well as upper bounds, are assumed to be known for the preemption durations and the non-preemptive code-execution durations; given such information, we derive algorithms for the optimal placement of preemption points in a manner that minimizes the typical overall running time (while continuing to guarantee, if needed, upper bounds on the worst-case over-all running time). Both off-line solutions (in which all preemption points are selected prior to run-time) and on-line solutions (where the selection more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10183410
Journal Name:
Proceedings of the International Conference on Real-Time Networks and Systems (RTNS)
Page Range or eLocation-ID:
198 to 208
National Science Foundation
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5. Abstract

We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_{i}{x}_{i}$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:

#SAT algorithms fornk-size$\mathcal { C}$$C$-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.

#SAT algorithms for$2^{n^{{\varepsilon }}}$${2}^{{n}^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$${2}^{n-{n}^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$\left(f\circ C\right)$-circuits of polynomial size.

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