Problems in sorting and graph algorithms
Dana Richards · 1984
Five disjoint problems are discussed. The first problem concerns the determination of optimal algorithms with respect to a new model for evaluating sorting algorithms. We did an exhaustive search for such algorithms. The second problem concerns a conjecture that every sorting algorithm on some input involves every key in O(log n) comparisons. We give partial results. The third problem concerns finding efficient algorithms for finding cycles of small fixed length in graphs. We give algorithms for general graphs and O(n log n) algorithms for cycles of length 5 or 6 in planar graphs. The fourth problem concerns the NP-completeness of a wire-routing problem. Specifically, the problem asks for vertex-disjoint paths connecting pairs of points in certain planar graphs. The fifth problem concerns automata traversing graphs in a myopic fashion. We study several cases and show when this can be done and when it is impossible.