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oai:drops-oai.dagstuhl.de:6415 2024-03-06T10:38:12Z ddc:004 open_access

Min-Sum Scheduling Under Precedence Constraints Schulz, Andreas S. Verschae, José scheduling approximation algorithms linear programming relaxations precedence constraints In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is that some jobs can only be processed after others. In this paper, we give the first approximation algorithms for min-sum scheduling with (nonnegative, non-decreasing) non-linear functions and general precedence constraints. In particular, for 1|prec|sum w_j f(C_j), we propose a polynomial-time universal algorithm that performs well for all functions f simultaneously. Its approximation guarantee is 2 for all concave functions, at worst. We also provide a (non-universal) polynomial-time algorithm for the more general case 1|prec|sum f_j(C_j). The performance guarantee is no worse than 2+epsilon for all concave functions. Our results match the best bounds known for the case of linear functions, a widely studied problem, and considerably extend the results for minimizing sum w_jf(C_j) without precedence constraints. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andreas S. Schulz and José Verschae 2016 Is Part Of LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2016.74 urn:nbn:de:0030-drops-64157 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.74 eng https://creativecommons.org/licenses/by/3.0/legalcode