Optimal Replica Placement in Tree Networks with QoS and Bandwidth Constraints and the Closest Allocation Policy

This paper deals with the replica placement problem on fully homogeneous tree networks known as the Replica Placement optimization problem. The client requests are known beforehand, while the number and location of the servers are to be determined. We investigate the latter problem using the Closest access policy when adding QoS and bandwidth constraints. We propose an optimal algorithm in two passes using dynamic programming.

💡 Research Summary

The paper tackles the replica placement problem (RPP) on fully homogeneous tree networks, where client request patterns are known in advance but the number and locations of replica servers must be chosen. Unlike most prior work that treats RPP as an NP‑hard problem on general graphs, the authors restrict the topology to a rooted tree and adopt the “Closest” allocation policy: each client must be served by the nearest replica in terms of hop distance (or latency). This policy naturally reduces client‑side latency but introduces tight coupling between server placement, quality‑of‑service (QoS) constraints (maximum allowable delay) and link bandwidth limits.

The authors formalize the problem as a three‑objective optimization: (1) minimize the total number of replicas, (2) satisfy every client’s QoS bound, and (3) keep the traffic on each tree edge below its capacity. They then present a two‑pass dynamic‑programming algorithm that solves the problem optimally in polynomial time.

In the first pass, a bottom‑up (root‑to‑leaf) traversal computes for each subtree a “required replica count” – a lower bound on how many replicas must be placed inside that subtree to meet all QoS and bandwidth constraints. This step also aggregates the total request volume of the subtree and records the maximum permissible distance from any client to a replica.

The second pass proceeds top‑down (leaf‑to‑root). For each node the algorithm maintains a DP table DP