Minimum Spillage Sequencing

The minimum spillage sequencing problem, which arises in real-time satellite signal data processing, requires a set of numbers to be arranged so as to minimize the “overflow” of the partial sums above an upper bound. We subject several heuristics to worst-case analysis, average-case analysis, and computational testing. The results demonstrate that the problem, though NP-hard, can be handled effectively. One of the highlights of the analysis is a tight upper bound on the fraction of overflow when the problem is solved to optimality, together with an O(n log n) “safe” heuristic which never exceeds this bound.