\u3cem\u3ek-k\u3c/em\u3e Routing, \u3cem\u3ek-k\u3c/em\u3e Sorting, and Cut Through Routing on the Mesh

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

Mesh Connected Computers With Multiple Fixed Buses: Packet Routing, Sorting and Selection

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k-k routing, k-k sorting, and cut through routing on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1-1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1-1 routing, k-k routing, cut through routing, and k-k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. In addition we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Our algorithms have considerably better time bounds than many existing best known algorithms

A Novel Solution to the Dynamic Routing and Wavelength Assignment Problem in Transparent Optical Networks

We present an evolutionary programming algorithm for solving the dynamic routing and wavelength assignment (DRWA) problem in optical wavelength-division multiplexing (WDM) networks under wavelength continuity constraint. We assume an ideal physical channel and therefore neglect the blocking of connection requests due to the physical impairments. The problem formulation includes suitable constraints that enable the algorithm to balance the load among the individuals and thus results in a lower blocking probability and lower mean execution time than the existing bio-inspired algorithms available in the literature for the DRWA problems. Three types of wavelength assignment techniques, such as First fit, Random, and Round Robin wavelength assignment techniques have been investigated here. The ability to guarantee both low blocking probability without any wavelength converters and small delay makes the improved algorithm very attractive for current optical switching networks.Comment: 12 Pages, IJCNC Journal 201

Randomized Algorithms For Packet Routing on the Mesh

Packet routing is an important problem of parallel computing since a fast algorithm for packet routing will imply 1) fast inter-processor communication, and 2) fast algorithms for emulating ideal models like PRAMs on fixed connection machines.There are three different models of packet routing, namely 1) Store and forward, 2) Multipacket, and 3) Cut through. In this paper we provide a survey of the best known randomized algorithms for store and forward routing, k-k routing, and cut through routing on the Mesh Connected Computers

Sample sort on meshes

This paper provides an overview of lower and upper bounds for mesh-connected processor networks. Most attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Grammatikakis, Hsu and Kraetzl on multicomputer routing, submitted to JPDC

Selection, Routing and Sorting on the Star Graph

We consider the problems of selection, routing and sorting on an n-star graph (with n! nodes), an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a \u27(k, l, k) chain network\u27) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n2) time. This algorithm is used as a subroutine in our other algorithms. In addition we offer an efficient deterministic sorting algorithm that runs in O(n3lg n) steps. Though an algorithm with the same time bound has been proposed before, our algorithm is very simple and is based on a different approach. We also show that sorting can be performed on the n star graph in time O(n3) and that selection of a set of uniformly distributed n keys can be performed in O(n2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n3) steps on the n-star graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph