Randomized online scheduling on two uniform machines

Leah Epstein; John Noga; Steve Seiden; Jiri Sgall; Gerhard Woeginger

Randomized online scheduling on two uniform machines

Leah Epstein, John Noga, Steve Seiden, Jiri Sgall, Gerhard Woeginger

Research output: Contribution to conference › Paper › peer-review

Abstract

We study the problem of online scheduling on two uniform machines with speeds 1 and s≥1. A φ≈1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s≥2, but does help for all s<2. We present a simple memoryless randomized algorithm that is (4-s)(1+s)/4≤1.5625 competitive. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.53 for any s. These algorithms are barely random, i.e., they use only a constant number of random bits, and similar methods yield also barely random algorithms for scheduling on two and three identical machines. Finally, we present a 1+s/(s²+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.

Original language	English
Pages	317-326
Number of pages	10
State	Published - 1999
Externally published	Yes
Event	Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA Duration: 17 Jan 1999 → 19 Jan 1999

Conference

Conference	Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms
City	Baltimore, MD, USA
Period	17/01/99 → 19/01/99

ASJC Scopus subject areas

Software
General Mathematics

Cite this

@conference{bca030967ff04444ab1705ac3001a9ab,

title = "Randomized online scheduling on two uniform machines",

abstract = "We study the problem of online scheduling on two uniform machines with speeds 1 and s≥1. A φ≈1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s≥2, but does help for all s<2. We present a simple memoryless randomized algorithm that is (4-s)(1+s)/4≤1.5625 competitive. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.53 for any s. These algorithms are barely random, i.e., they use only a constant number of random bits, and similar methods yield also barely random algorithms for scheduling on two and three identical machines. Finally, we present a 1+s/(s2+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.",

author = "Leah Epstein and John Noga and Steve Seiden and Jiri Sgall and Gerhard Woeginger",

year = "1999",

language = "English",

pages = "317--326",

note = "Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms ; Conference date: 17-01-1999 Through 19-01-1999",

}

TY - CONF

T1 - Randomized online scheduling on two uniform machines

AU - Epstein, Leah

AU - Noga, John

AU - Seiden, Steve

AU - Sgall, Jiri

AU - Woeginger, Gerhard

PY - 1999

Y1 - 1999

N2 - We study the problem of online scheduling on two uniform machines with speeds 1 and s≥1. A φ≈1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s≥2, but does help for all s<2. We present a simple memoryless randomized algorithm that is (4-s)(1+s)/4≤1.5625 competitive. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.53 for any s. These algorithms are barely random, i.e., they use only a constant number of random bits, and similar methods yield also barely random algorithms for scheduling on two and three identical machines. Finally, we present a 1+s/(s2+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.

AB - We study the problem of online scheduling on two uniform machines with speeds 1 and s≥1. A φ≈1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s≥2, but does help for all s<2. We present a simple memoryless randomized algorithm that is (4-s)(1+s)/4≤1.5625 competitive. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.53 for any s. These algorithms are barely random, i.e., they use only a constant number of random bits, and similar methods yield also barely random algorithms for scheduling on two and three identical machines. Finally, we present a 1+s/(s2+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.

UR - http://www.scopus.com/inward/record.url?scp=0032785086&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0032785086

SP - 317

EP - 326

T2 - Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 17 January 1999 through 19 January 1999

ER -

Randomized online scheduling on two uniform machines

Abstract

Conference

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this