Edge Congestion Research Articles

A global router with a theoretical bound on the optimal solution

The global routing problem is formulated as a multiterminal, multicommodity flow problem with integer flows, An E-optimal 2-terminal multicommodity flow algorithm with fractional flows is extended to handle multiterminal commodities, Our adaptation of this network flow algorithm seeks to maximize overall routability by minimizing edge congestion as opposed to conventional techniques which usually seek to minimize wire length. We show that under certain conditions, our approach derives an approximate optimal solution. We apply a randomized rounding procedure to derive an integer solution from the fractional multicommodity flow solution. Experimental results demonstrate that this network flow algorithm can be realistically used to route industrial sized circuits with reduced congestion.

Simulation of Binary Trees and X-Trees on Pyramid Networks

Traditionally, pyramid machines have been used for image processing problems. In this paper, we examine techniques for extending the use of pyramid networks. In particular, we show (1) every complete binary tree is a subgraph of its optimum pyramid, (2) the X-tree is not a subgraph of its optimum pyramid, but (3) every X-tree can be embedded into its optimum pyramid with dilation 2 and edge congestion 2, and (4) every binary tree can be embedded into a pyramid with constant dilation and constant expansion.

A parallel algorithm for an efficient mapping of grids in hypercubes

The authors parallelize the embedding strategy for mapping any two-dimensional grid into its optimal hypercube with minimal dilation. The parallelization allows each hypercube node to independently determine, in constant time, which grid node it will simulate and the communication paths it will take to reach the hypercube nodes that simulate its grid-neighbors. The paths between grid-neighbors are chosen in such a way as to curb the congestion at each hypercube node and across each hypercube edge. Explicity, the node congestion for the embedding is at most 6, one above optimal, while the edge congestion is at most 5. >