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A New Broadcast Model for Several Network Topologies

Hongbo Lu, Junsung Hwang, Bernard Tenreiro, Nabila Jaman Tripti, Darren Hamilton, Yuefan Deng

TL;DR

This work introduces Broadcast by Balanced Saturation (BBS), a topology-aware, deterministic broadcast framework that maximizes edge utilization to minimize latency across arbitrary undirected network topologies. It develops a formal broadcast model, proves that a balanced solution $A^{\text{b}}$ optimizes arrival times within the continuum-limit class, and derives a practical BBS-induced algorithm (BIA) via cyclic scheduling on a colored multigraph. Theoretical bounds on initialization, steady-state, and overall broadcast times are provided, along with storage and scheduling complexity, and the approach is validated through extensive simulations on grids and higher-dimensional topologies where BBS consistently outperforms baselines, especially for large data sizes. The results suggest BBS offers a versatile, scalable framework with potential for real-world deployment and extensions to more complex topologies and collective operations.

Abstract

We present Broadcast by Balanced Saturation (BBS), a general broadcast algorithm designed to optimize communication efficiency across diverse network topologies. BBS maximizes node utilization, addressing challenges in broadcast operations such as topology constraints, bandwidth limitations, and synchronization overhead, particularly in large-scale systems like supercomputers. The algorithm ensures sustained activity with nodes throughout the broadcast, thereby enhancing data propagation and significantly reducing latency. Through a precise communication cycle, BBS provides a repeatable, streamlined, stepwise broadcasting framework. Simulation results across various topologies demonstrate that the BBS algorithm consistently outperforms common general broadcast algorithms, often by a substantial margin. These findings suggest that BBS is a versatile and robust framework with the potential to redefine broadcast strategies across network topologies.

A New Broadcast Model for Several Network Topologies

TL;DR

This work introduces Broadcast by Balanced Saturation (BBS), a topology-aware, deterministic broadcast framework that maximizes edge utilization to minimize latency across arbitrary undirected network topologies. It develops a formal broadcast model, proves that a balanced solution optimizes arrival times within the continuum-limit class, and derives a practical BBS-induced algorithm (BIA) via cyclic scheduling on a colored multigraph. Theoretical bounds on initialization, steady-state, and overall broadcast times are provided, along with storage and scheduling complexity, and the approach is validated through extensive simulations on grids and higher-dimensional topologies where BBS consistently outperforms baselines, especially for large data sizes. The results suggest BBS offers a versatile, scalable framework with potential for real-world deployment and extensions to more complex topologies and collective operations.

Abstract

We present Broadcast by Balanced Saturation (BBS), a general broadcast algorithm designed to optimize communication efficiency across diverse network topologies. BBS maximizes node utilization, addressing challenges in broadcast operations such as topology constraints, bandwidth limitations, and synchronization overhead, particularly in large-scale systems like supercomputers. The algorithm ensures sustained activity with nodes throughout the broadcast, thereby enhancing data propagation and significantly reducing latency. Through a precise communication cycle, BBS provides a repeatable, streamlined, stepwise broadcasting framework. Simulation results across various topologies demonstrate that the BBS algorithm consistently outperforms common general broadcast algorithms, often by a substantial margin. These findings suggest that BBS is a versatile and robust framework with the potential to redefine broadcast strategies across network topologies.
Paper Structure (11 sections, 2 theorems, 18 equations, 11 figures, 6 tables, 1 algorithm)

This paper contains 11 sections, 2 theorems, 18 equations, 11 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Broadcast Model
  3. Definitions
  4. Occupancy Constraints
  5. The Balanced Solution
  6. Performance Analysis
  7. Numerical Simulations
  8. Setup
  9. Results and Discussions
  10. Conclusions and Future Work
  11. Performance Figures

Key Result

Theorem 1

For any algorithm A, there exists $A^{\mathrm{cc}} \in \mathrm{CC}$ such that $T(A^{\mathrm{cc}}) \leq T(A)$.

Figures (11)

  • Figure 1: Visual representation of exclusivity constraints
  • Figure 2: BIA derivation on a $4 \times 4$ grid with node $0$ as the root. $G_1$: Initial $4 \times 4$ grid topology. $G_2$: All $O_{i,j}$ are obtained by solving the balanced solution. $G_3$: Multiply $l$ to each $O_{i,j}$. $G_4$: Integer weights on directed edges are converted to undirected edges in the multigraph. $G_5$: Edge coloring of the multigraph, where the number of colors equals the maximum degree of the multigraph and corresponds to the number of frames. Each frame then undergoes post-processing.
  • Figure 3: BIA cyclic frame factorization on the $4\times4$ grid, where $d_\text{m}=8$ and node $0$ is the root. In each step, if there is an arrow between nodes, a packet is sent in that direction.
  • Figure 4: Number of active edges per step on the $16 \times 64$ grid topology with $N$ = 2500
  • Figure 5: Comparison of the time steps to complete each broadcast algorithm on a square grid topology with given $P$
  • ...and 6 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof : Proof:
  • Theorem 2
  • proof : Proof:
  • proof : Proof:
  • proof : Proof: