Algorithms for rectilinear optimal multicast tree problem

Abstract

Given a point s called the signal source and a set D of points called the sinks, a rectilinear multicast tree is defined as a tree T = (V, E) such that s ε V, D ⊆ V, and the length of each path on T from the source s to a sink t equals the L1-distance from s to t. A rectilinear multicast tree is said to be optimalif the total length of T is minimized. The optimal multicast tree (OMT) problem in general is NP-complete [1, 2, 4], while the complexity of the rectilinear version is still open. In this paper, we present algorithms to solve the rectilinear optimal multicast tree (ROMT) problem. Our algorithms require O(n 3k) and O(n23n) time, where n denotes |D| and k is the number of dominating layers defined by s.