TR-95-22: Approximate Maxima Finding of Continuous Functions under Restricted Budget

A function is distributed among nodes of a graph in a continuous way, i.e., such that the dierence between values stored at adjacent nodes is small. The goal is to nd a node of maximum value by probing some nodes under a restricted budget. Every node has an associated cost which has to be paid for probing it and a probe reveals the value of the node. If the total budget is too small to allow probing every node, it is impossible to nd the maximum value in the worst case. Hence we seek an Approximate Maxima Finding (AMF) algorithm that oers the best worst-case guarantee g, i.e., for any continuous distribution of values it nds a node whose value diers from the maximum value by at most g.Approximate Maxima Finding in graphs is related to a generalization of the multi-center problem and we get new results for this problem as well. For example, we givea polynomial algorithm to nd a minimum cost solution for the multicenter problem on a tree, with arbitrary node costs.