A unified approach to scheduling on unrelated parallel machines
Abstract
We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming-, quadratic programming-, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. This algorithm leads to the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria; (ii) better-than-two approximation guarantees for scheduling to minimize the L p norm of the vector of machine-loads, for all 1 < p < ∞; and (iii) the first constant-factor multicriteria approximation algorithms that can handle the weighted completion-time and any given collection of integer L p norms. Our algorithm has a natural interpretation as a melding of linear-algebraic and probabilistic approaches. Via this view, it yields a common generalization of rounding theorems due to Karp et al. [1987] and Shmoys & Tardos [1993], and leads to improved approximation algorithms for the problem of scheduling with resource-dependent processing times introduced by Grigoriev et al. [2007].
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 01, 2009
- Source ID
- 10.1145/1552285.1552289
Entities
People
- Aravind Srinivasan
- Madhav Marathe
- Srinivasan Parthasarathy
- V. S. Anil Kumar
Organizations
- Centers for Disease Control and Prevention
- Defense Threat Reduction Agency
- Division of Computer and Network Systems
- Division of Social and Economic Sciences
- International Business Machines Corporation (Armonk, NY)
- National Institute of General Medical Sciences
- National Science Foundation
- University of Maryland
- Virginia Tech