Maximum Bounded Rooted-Tree Packing Problem

Abstract

Given a graph and a root, the Maximum Bounded Rooted-Tree Packing (MBRTP) problem aims at finding K rooted-trees that span the largest subset of vertices, when each vertex has a limited outdegree. This problem is motivated by peerto-peer streaming overlays in under-provisioned systems. We prove that the MBRTP problem is NP-complete. We present two polynomial-time algorithms that computes an optimal solution on complete graphs and trees respectively.

Bounded-degree rooted tree and TDI-ness

“…Note that inequalities (12) and inequalities( 13) are special cases of connectivity inequalities (8) and upload capacity inequalities (10) respectively. Let the polytope defined by the linear system composed of ( 12)-( 16) be…”

“…The problem, considered in [2] and called the Maximum Bounded-Degree Rooted Tree (MBDRT) problem, then consists of finding a rooted tree which respects the degree constraints and maximizes the number of nodes it contains. In [10], the MBDRT problem was showed to be an NP-hard combinatorial optimization problem by reducing the 3-SAT problem [8] to it, and polynomial-time algorithms were given on certain classes of graphs such as trees, cycles and complete graphs.…”