Single Machine Precedence Constrained Scheduling Is a Vertex Cover Problem
In this paper we study the single machine precedence constrained scheduling problem of minimizing the sum of weighted completion time. Specifically, we settle an open problem first raised by Chudak & Hochbaum and whose answer was subsequently conjectured by Correa & Schulz.
The most significant implication of our result is that the addressed scheduling problem is a special case of the vertex cover problem. This will hopefully be an important step towards proving that the two problems behave identically in terms of approximability.
As a consequence of our result, previous results for the scheduling problem can be explained, and in some cases improved, by means of vertex cover theory. For example, our result implies the existence of a polynomial time algorithm for the special case of two-dimensional partial orders. This considerably extends Lawler’s result from 1978 for series-parallel orders.
KeywordsSchedule Problem Single Machine Precedence Constraint Vertex Cover Single Machine Schedule
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