Deterministic monotone algorithms for scheduling on related machines
We consider the problem of designing monotone deterministic algorithms for scheduling tasks on related machines in order to minimize the makespan. Several recent papers showed that monotonicity is a fundamental property to design truthful mechanisms for this scheduling problem. We give both theoreti...
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| Vydané v: | Theoretical computer science Ročník 406; číslo 3; s. 173 - 186 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
31.10.2008
|
| Predmet: | |
| ISSN: | 0304-3975, 1879-2294 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | We consider the problem of designing monotone deterministic algorithms for scheduling tasks on related machines in order to minimize the makespan. Several recent papers showed that monotonicity is a fundamental property to design truthful mechanisms for this scheduling problem.
We give both theoretical and experimental results. First of all we consider the case of two machines when speeds of the machines are restricted to be powers of a given constant
c
>
0
. We prove that algorithm
Largest Processing Time (
LPT) is monotone for any
c
≥
2
while it is not monotone for
c
≤
1.78
; algorithm
List Scheduling (
LS), instead, is monotone only for
c
>
2
.
In the case of
m
>
2
machines we restrict our attention to the class of “greedy-like” monotone algorithms defined in [Vincenzo Auletta, Roberto De Prisco, Paolo Penna, Giuseppe Persiano, Deterministic truthful approximation mechanisms for scheduling related machines, in: Proceedings of 21st Annual Symposium on Theoretical Aspects of Computer Science. STACS ’04, in: Lecture Notes in Computer Science, vol. 2996, Springer, 2004, pp. 608–619]. It has been shown that greedy-like monotone algorithms can be used to design a family of
2
+
ε
-approximate truthful mechanisms. In particular, in [Vincenzo Auletta, Roberto De Prisco, Paolo Penna, Giuseppe Persiano, Deterministic truthful approximation mechanisms for scheduling related machines, in: Proceedings of 21st Annual Symposium on Theoretical Aspects of Computer Science. STACS ’04, in: Lecture Notes in Computer Science, vol. 2996, Springer, 2004, pp. 608–619], the greedy-like algorithm
Uniform is proposed and it is proved that it is monotone when machine speeds are powers of a given integer constant
c
>
0
. In this paper we propose a new algorithm, called
Uniform_RR, that is still monotone when speeds are powers of a given integer constant
c
>
0
and we prove that its approximation factor is not worse than that of
Uniform. We also experimentally compare the performance of
Uniform,
Uniform_RR,
LPT, and several other monotone and greedy-like heuristics. |
|---|---|
| ISSN: | 0304-3975 1879-2294 |
| DOI: | 10.1016/j.tcs.2008.06.050 |