TY - GEN
T1 - A PTAS for minimizing weighted completion time on uniformly related machines (extended abstract)
AU - Chekuri, Chandra
AU - Khanna, Sanjeev
PY - 2001
Y1 - 2001
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 -