— We design network topologies and routing strategies which optimize several measures simultaneously: low cost, small routing diameter , bounded degree and low congestion. This set of design issues is broader than traditional network design and hence, our work is useful and relevant to a set of traditional and emerging design problems. Surprisingly, a simple idea from the research on small-world models, inspires a fruitful approach and useful techniques here. Starting with a simple model we consider adding long links to an n×n grid graph. Ideally, for a given budget to buy additional long links, we consider mechanisms for choosing links such that the routing diameter is small enough (poly-log of n) while the congestion ratio (between the most used link and the average one) is minimized, assuming uniform traffic between any two of the n2 nodes. We show that by adding O(1) long links to each node we achieve an almost logarithmic routing diameter and maintain a near optimal trade-off ...
Van Nguyen, Charles U. Martel