List Ranking on Interconnection Networks

The list-ranking problem is considered for parallel computers which communicate through an interconnection network. Each PU holds k nodes of a set of singly linked lists. An easy randomized algorithm gives a considerable improvement over earlier ones. For a large class of networks, the algorithm takes only twice the number of steps required by a k-k routing. The only conditions are that: (1) k = !(k), where k is so large that the time consumption of k-k routing is determined by the bisection bound, and (2) the routing time slightly increases with the number of PUs in the network. For special networks we can prove stronger results. Particularly, for n n meshes, the list ranking problem is solved in (1=2+o(1))kn steps, if k = !(1). For hypercubes with N PUs, assuming all-port communication, the algorithm requires only (2 + o(1)) k steps, if k = !(log 2 N). We show that list ranking requires at least the time required for k-k routing. So, the results are within a factor two from optimal. For meshes we even match the lower bound up to lower-order terms.