Optimal Randomized Algorithms for Local Sorting and Set-Maxima

We present randomized algorithms for two sorting problems. In the local sorting problem, a graph is given in which each vertex is assigned an element of a total order, and the task is to determine the relative order of every pair of adjacent vertices. In the set-maxima problem, a collection of sets whose elements are drawn from a total order is given, and the task is to determine the maximum element in each set. We describe lower bounds for the problems in the comparison model, and show that the algorithms are optimal within a constant factor. Key words. sorting, randomized algorithms, comparison model, partial order, graph algorithms

• Type: Conference
• Year: 1990
• Where: STOC
• Authors: Wayne Goddard, Valerie King, Leonard J. Schulman
• Keywords: Algorithms, Local Sorting Problem, Randomized Algorithms, STOC 1990, Total Order