Maximum Bounded Rooted-Tree Packing Problem

TL;DR

This paper investigates the NP-complete problem of packing K rooted-trees with degree constraints in a graph, providing polynomial algorithms for special graph classes and highlighting its relevance to peer-to-peer streaming systems.

Contribution

It introduces the Maximum Bounded Rooted-Tree Packing problem, proves its NP-completeness, and offers polynomial algorithms for complete graphs and trees.

Findings

Proves MBRTP is NP-complete.

Provides polynomial algorithms for complete graphs.

Provides polynomial algorithms for trees.

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 peer-to-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.