## Abstract

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 Maxima 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.

Original language | English |
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Pages (from-to) | 151-162 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 203 |

Issue number | 1 |

DOIs | |

State | Published - 6 Aug 1998 |

Externally published | Yes |

### Bibliographical note

Funding Information:* Corresponding author. E-mail: peleg@wisdom.weizmann.ac.il. ’ Research supported in part by NSERC (Natural Sciences and Engineering Research Council of Canada) grants. 2 Part of this research was performed while this author was visiting Carleton University as a COGNOS scholar. Supported in part by a grant from the Israel Science Foundation and by a grant from the Israel Ministry of Science and Art.

## Keywords

- Approximate maxima finding
- Multicenter problems
- WWW search