Technical Reports (CIS)

Document Type

Technical Report

Date of this Version

October 1993


University of Pennsylvania Department of Computer and Information Sciences Technical Report No. MS-CIS-91-93.


In this paper we present randomized algorithms for k-k routing, k-k sorting, and cut through routing. The stated resource bounds hold with high probability. The algorithm for k-k routing runs in [k/2]n+o(kn) steps. We also show that k-k sorting can be accomplished within [k/2] n+n+o(kn) steps, and cut through routing can be done in [3/4]kn+[3/2]n+o(kn) steps. The best known time bounds (prior to this paper) for all these three problems were kn+o(kn).

[kn/2] is a known lower bound for all the three problems (which is the bisection bound), and hence our algorithms are very nearly optimal. All the above mentioned algorithms have optimal queue length, namely k+o(k). These algorithms also extend to higher dimensional meshes.



Date Posted: 30 July 2007