Optimal algorithms and approximation algorithms for replica placement with distance constraints in tree networks

In this paper, we study the problem of replica placement in tree networks subject to server capacity and distance constraints. The client requests are known beforehand, while the number and location of the servers are to be determined. The Single policy enforces that all requests of a client are served by a single server in the tree, while in the Multiple policy, the requests of a given client can be processed by multiple servers, thus distributing the processing of requests over the platform. For the Single policy, we prove that all instances of the problem are NP-hard, and we propose approximation algorithms. The problem with the Multiple policy was known to be NP-hard with distance constraints, but we provide a polynomial time optimal algorithm to solve the problem in the particular case of binary trees when no request exceeds the server capacity

Approximation algorithms for a hierarchically structured bin packing problem

In this paper we study a variant of the bin packing problem in which the items to be packed are structured as the leaves of a tree. The problem is motivated by document organization and retrieval. We show that the problem is NP-hard and we give approximation algorithms for the general case and for the particular case in which all the items have the same size