TY - GEN

T1 - A PTAS for minimizing weighted completion time on uniformly related machines (extended abstract)

AU - Chekuri, Chandra

AU - Khanna, Sanjeev

PY - 2001/12/1

Y1 - 2001/12/1

N2 - We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p/s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + ε).

AB - We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p/s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + ε).

KW - Aerage completion time

KW - Polynomial time approximation scheme

KW - Sheduling

KW - Uiformly related machines

KW - Wighted completion time

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M3 - Conference contribution

AN - SCOPUS:84879514907

SN - 3540422870

SN - 9783540422877

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 848

EP - 861

BT - Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings

T2 - 28th International Colloquium on Automata, Languages and Programming, ICALP 2001

Y2 - 8 July 2001 through 12 July 2001

ER -