A Network Flow Approach to Solving Weighted Processor-Optimal Allocation Problems

Given a set of operations specified by their execution time intervals {[ai,zi)|i=1, ..., n}, where ai<zi, a processor-optimal allocation (POA) problem is to allocate the minimum number of processors to execute these operations, where any two operations [aj,zj) and [ak,zk) executed by a processor have the property of either zj≤ak or zk≤aj. A weighted version of the POA problem is to find a processor-optimal allocation with a minimal value of a linearly weighted function. There are many existing algorithms for solving these allocation problems. However, these algorithms are having time complexity of an exponential function, solving non-weighted POA problem, or achieving only locally optimal solutions. On the base of the minimum-cost network flow model, this paper proposes an algorithm to optimally solve the weighted POA problem in polynomial time.