ABSTRACT
This paper presents a theoretical framework analyzing optimality gaps in relaxation-based approximation algorithms for scheduling problems, establishing bounds across LP, SDP, and Lagrangian relaxations, and discussing their limitations.
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Key findings
Unified framework for analyzing optimality gaps across LP, SDP, and Lagrangian relaxations.
Tight integrality gap bounds of 2 for assignment LP in makespan minimization.
Characterization of conditions for stronger relaxations to achieve improved bounds.
Establishment of a hierarchy of relaxation strengths and their intrinsic limitations.
Limitations & open questions
Further research needed to close the gap between theoretical upper and lower bounds.