An Optimal Algorithm for Partial Order Multiway Search

Abstract

Partial order multiway search (POMS) is an important problem that finds use in crowdsourcing, distributed file systems, software testing, etc. In this problem, a game is played between an algorithm A and an oracle, based on a directed acyclic graph G known to both parties. First, the oracle picks a vertex t in G called the target; then, A aims to figure out which vertex is t by probing reachability. In each probe, A selects a set Q of vertices in G whose size is bounded by a pre-agreed value k, and the oracle then reveals, for each vertex q 2 Q, whether q can reach the target in G. The objective of A is to minimize the number of probes. This article presents an algorithm to solve POMS in O(log1+k n + d k log1+d n) probes, where n is the number of vertices in G, and d is the largest out-degree of the vertices in G. The probing complexity is asymptotically optimal.