Approximate maxima finding of continuous functions under restricted budget

✍ Scribed by Evangelos Kranakis; Danny Krizanc; Andrzej Pelc; David Peleg

• Book ID: 104326395
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 777 KB
• Volume: 203
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(97)00293-4

✦ Synopsis

A function is distributed among nodes of a graph in a "continuous" (or "slowly changing") way, i.e., such that the difference between values stored at adjacent nodes is small. The goal is to find 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 find the maximum value in the worst case. Hence we seek an Approximate Maximu Finding (AMF) algorithm that offers the best worst-case guarantee g, i.e., for any continuous distribution of values it finds a node whose value differs from the maximum value by at most g.

AMF in graphs is related to a generalization of the multicenter problem and we get new results

for this problem as well. For example, we give a polynomial algorithm to find a minimum cost solution for the multicenter problem on a tree, with arbitrary node costs.