# Toward a general theory of unicast-based multicast communication

## Abstract

Multicast, also known as one-to-many communication, is the problem of sending a message from a single source node to several destination nodes. In this paper, we study the problem of implementing multicasts via a technique called Unicast-Based Multicast (UBM). In particular, we focus on the problem of finding optimal UBM calling schedules for *arbitrary* topologies using restricted *inclusive* routing schemes (a natural class of restricted routing schemes which includes most practically implemented restricted routing schemes) given *source limited* routing information. Previous work has focused on finding optimal UBM calling schedules for *arbitrary* topologies using free routing schemes given complete routing information and *specific* topologies using specific restricted routing schemes given complete routing information. We first show that implementing UBM in arbitrary topologies with restricted routing schemes is fundamentally different than implementing UBM in arbitrary topologies with free routing schemes. We then develop the Smart Centroid Algorithm, a polynomial time approximation algorithm which produces UBM calling schedules that are at most four times as long as the optimal UBM calling schedule for arbitrary topologies using restricted inclusive routing schemes given source limited routing information. The question of determining the NP-hardness of producing optimal UBM calling schedules for arbitrary topologies using any restricted routing scheme remains open.

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