On the approximability of an interval scheduling problem

Abstract

In this paper we consider a general interval scheduling problem. The problem is a natural generalization of finding a maximum independent set in an interval graph. We show that, unless 𝒫=𝒩𝒫, this maximization problem cannot be approximated in polynomial time within arbitrarily good precision. On the other hand, we present a simple greedy algorithm that delivers a solution with a value of at least 1/2 times the value of an optimal solution. Finally, we investigate the quality of an LP‐relaxation of a formulation for the problem, by establishing an upper bound on the ratio between the value of the LP‐relaxation and the value of an optimal solution. Copyright © 1999 John Wiley & Sons, Ltd.

The temporal explorer who returns to the base

“…JISP(k) is a well-studied problem in the Scheduling community, with several known complexity results. In particular, Spieksma [21] showed a 2-approximation for the problem, later improved to a 1.582-approximation by Chuzhoy et al [9]. This immediately implies a 1.582-approximation algorithm for MaxStarExp(k); we use the latter to conclude on the APX-completeness 6 of MaxStarExp(k).…”

Interval scheduling and colorful independent sets

“…We complement known polynomial-time approximability results (Spieksma 1999;Chuzhoy et al 2006) for Job Interval Selection with parameterized complexity results and extend the tractability results by Halldórsson and Karlsson (2006) in several ways:…”

“…Job Interval Selection was introduced by Nakajima and Hakimi (1982) and was shown APX-hard by Spieksma (1999), who also provided a ratio-2 greedy approximation algorithm. Chuzhoy et al (2006) improved this to a ratio-1.582 approximation algorithm.…”

Interval Scheduling and Colorful Independent Sets

“…Results for Job Interval Selection. We complement known polynomialtime approximability results (Spieksma, 1999;Chuzhoy et al, 2006) for Job Interval Selection with parameterized complexity results and extend the tractability results by Halldórsson and Karlsson (2006) in several ways:…”