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Algorithms and Time Complexity of the Request-Service Problem.
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2008-12-31 , DOI: 10.1007/s10878-008-9202-9
Chunmei Liu 1 , Legand Burge , Ajoni Blake
Affiliation  

Given a number of users each of which provides a set of services with a cost for each service and has a set of requests to be satisfied, the goal of the request-service problem is to find a feasible solution that satisfies all requests of each user with minimum cost. In addition, a feasible solution must satisfy an additional constraint. Specifically, if user A provides a service to user B, B should provide a service back to A either directly or indirectly through other users. In this paper, we studied the complexity of this problem. We show that there exists a polynomial time algorithm that can compute a feasible solution with minimum cost if such a solution exists. However, if a feasible solution does not exist, the problem of maximizing the number of satisfied users (i.e., all requests of the users are satisfied) is NP-hard.

中文翻译:

请求服务问题的算法和时间复杂度。

给定多个用户,每个用户提供一组服务,每个服务都有成本,并有一组要满足的请求,请求服务问题的目标是找到满足每个用户所有请求的可行解决方案以最低的成本。此外,可行解必须满足附加约束。具体来说,如果用户 A 向用户 B 提供服务,则 B 应直接或通过其他用户间接向 A 提供服务。在本文中,我们研究了这个问题的复杂性。我们表明存在多项式时间算法,如果存在这样的解决方案,它可以以最小的成本计算可行的解决方案。然而,如果不存在可行的解决方案,最大化满足用户的数量(即满足用户的所有请求)的问题是NP-hard的。
更新日期:2008-12-31
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