Showing papers by "Sunil M. Shende published in 2001"

Static Frequency Assignment in Cellular Networks

Abstract: A cellular network is generally modeled as a subgraph of the triangular lattice. In the static frequency assignment problem, each vertex of the graph is a base station in the network, and has associated with it an integer weight that represents the number of calls that must be served at the vertex by assigning distinct frequencies per call. The edges of the graph model interference constraints for frequencies assigned to neighboring stations. The static frequency assignment problem can be abstracted as a graph multicoloring problem. We describe an efficient algorithm to multicolor optimally any weighted even or odd length cycle representing a cellular network. This result is further extended to any outerplanar graph. For the problem of multicoloring an arbitrary connected subgraph of the triangular lattice, we demonstrate an approximation algorithm which guarantees that no more than 4/3 times the minimum number of required colors are used. Further, we show that this algorithm can be implemented in a distributed manner, where each station needs to have knowledge only of the weights at a small neighborhood.

Approximate Hotlink Assignment

Abstract: Consider a directed rooted tree T = (V,E) of maximal degree d representing a collection V of web pages connected via a set E of links all reachable from a source home page, represented by the root of T. Each leaf web page carries a weight representative of the frequency with which it is visited. By adding hotlinks, shortcuts from a node to one of its descendents, we are interested in minimizing the expected number of steps needed to visit the leaf pages from the home page. We give an O(N2) time algorithm for assigning hotlinks so that the expected number of steps to reach the leaves from the root of the tree is at most H(p)/log(d+1)-(d/(d+1)) log d + d+1/d, where H(p) is the entropy of the probability (frequency) distribution p = on the N leaves of the given tree, i.e., pi is the weight on the ith leaf. The best known lower bound for this problem is H(p)/log(d+1). Thus our algorithm approximates the optimal hotlink assignment to within a constant for any fixed d.