We propose an approximation algorithm for the problem of Fault-Tolerant Facility Location which is implemented in a distributed and asynchronous manner within O(n) rounds of communication. Here n is the number of vertices in the network. As far as we know, the performance guarantee of similar algorithms (centralized) remains unknown except a special case where all cities have a uniform connectivity requirement. In this paper, we assume the shortest-path routing scheme deployed, as well as a constant (given) size of R, which represents the distinct levels of fault-tolerant capability provided by the system (i. e distinct connectivity requirements), and prove that the cost of our solution is no more than |R| ÃÂ÷ F* + 2 ÃÂ÷ C* in the general case, where F* and C* are respectively the facility cost and connection cost in an optimal solution. Further more, extensive numerical experiments showed that the quality of our solutions is comparable to the optimal solutions when |R| is no more than 10.
展开▼
机译:我们针对容错设施位置问题提出了一种近似算法,该算法在O(n)个回合通信中以分布式和异步方式实现。这里n是网络中的顶点数。据我们所知,除了所有城市都有统一的连通性要求的特殊情况外,类似算法(集中式)的性能保证仍然未知。在本文中,我们假设部署了最短路径路由方案,并且R的大小恒定(给定),R表示系统提供的不同级别的容错能力(即不同的连通性要求),并且证明我们的解决方案的成本不超过| R |在通常情况下,F * + 2 * C *,其中F *和C *分别是最佳解决方案中的设施成本和连接成本。此外,大量的数值实验表明,当| R |时,我们的解决方案的质量与最佳解决方案相当。不超过10。
展开▼