A General Framework for Approximating Min Sum Ordering Problems

Felix Happach, Lisa Hellerstein, Thomas Lidbetter

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider a large family of problems inwhich an ordering (or,more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of min sum set cover, several scheduling and search problems, and problems in Boolean function evaluation. We define a new problem, called the min sum ordering problem (MSOP), which generalizes all these problems using a cost and a weight function defined on subsets of a finite set. Assuming a polynomial time α-approximation algorithm for the problem of finding a subset whose ratio of weight to cost is maximal, we show that under very minimal assumptions, there is a polynomial time 4α-approximation algorithm for MSOP. This approximation result generalizes a proof technique used for several distinct problems in the literature. We apply this to obtain a number of new approximation results.

Original languageEnglish (US)
Pages (from-to)1437-1452
Number of pages16
JournalINFORMS Journal on Computing
Issue number3
StatePublished - May 2022

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


  • Boolean function evaluation
  • approximation algorithms
  • min sum set cover
  • scheduling
  • search theory


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