Ordering Problems Approximated: Single-Processor Scheduling and Interval Graph Completion

In this paper, we give the first polynomial time approximation algorithms for two problems in combinatorial optimization. The first problem is single-processor scheduling to minimize weighted sum of completion times, subject to precedence constraints. The second problem, interval graph completion, is finding a minimum-size interval graph containing the input graph as a subgraph. Both problems are NP-complete; our algorithms output solutions that are within a polylogarithmic factor of optimal. To achieve these bounds, we make use of a technique developed and first applied by Leighton and Rao [12], together with a technique of Hansen [5].

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