A Randomized Queueless Algorithm for Breadth-First Search

First Come First Served is a policy that is accepted for implementing fairness in a number of application domains such as scheduling in Operating Systems [28, 11], scheduling web requests and so on. We also have orthogonal applications of FCFS policies in proving correctness of search algorithms such as Breadth-First Search and the Bellman-Ford FIFO implementation for finding single-source shortest paths [2], program verification [12] and static analysis [25, 24]. The principal data structure used in implementing FCFS policies is the queue, which is realized either through a circular array or a linked list. The question of interest then, is whether queues are required to implement FCFS policies; this paper provides empirical evidence answering this question in the negative. The principal contribution of this paper is the development of a randomized algorithm to implement approximate FCFS policies without queues. The techniques that are developed in this paper find direct applications in program verification, model checking, in the implementation of distributed queues and in the design of incremental algorithms for shortest path problems.