IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Assigning Proximity Facilities for Gatherings
Shin-ichi NAKANO
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2024 Volume E107.D Issue 3 Pages 383-385

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Abstract

In this paper we study a recently proposed variant of the r-gathering problem. An r-gathering of customers C to facilities F is an assignment A of C to open facilities F'F such that r or more customers are assigned to each open facility. (Each facility needs enough number of customers to open.) Given an opening cost op(f) for each fF, and a connecting cost co(c,f) for each pair of cC and fF, the cost of an r-gathering A is max{maxcC{co(c, A(c))}, maxfF'{op(f)}}. The r-gathering problem consists of finding an r-gathering having the minimum cost. Assume that F is a set of locations for emergency shelters, op(f) is the time needed to prepare a shelter fF, and co(c,f) is the time needed for a person cC to reach assigned shelter f=A(c)∈F. Then an r-gathering corresponds to an evacuation plan such that each open shelter serves r or more people, and the r-gathering problem consists of finding an evacuation plan minimizing the evacuation time span. However in a solution above some person may be assigned to a farther open shelter although it has a closer open shelter. It may be difficult for the person to accept such an assignment for an emergency situation. Therefore, Armon considered the problem with one more additional constraint, that is, each customer should be assigned to a closest open facility, and gave a 9-approximation polynomial-time algorithm for the problem. We have designed a simple 3-approximation algorithm for the problem. The running time is O(r|C||F|).

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