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Paralleling and Accelerating Arc Consistency Enforcement with Recurrent Tensor Computations

Mingqi Yang

TL;DR

A new arc consistency enforcement paradigm is proposed that transforms arc consistency enforcement into recurrent tensor operations, which fully leverages the power of parallelization and GPU, and therefore is extremely efficient on large and densely connected constraint networks.

Abstract

We propose a new arc consistency enforcement paradigm that transforms arc consistency enforcement into recurrent tensor operations. In each iteration of the recurrence, all involved processes can be fully parallelized with tensor operations. And the number of iterations is quite small. Based on these benefits, the resulting algorithm fully leverages the power of parallelization and GPU, and therefore is extremely efficient on large and densely connected constraint networks.

Paralleling and Accelerating Arc Consistency Enforcement with Recurrent Tensor Computations

TL;DR

A new arc consistency enforcement paradigm is proposed that transforms arc consistency enforcement into recurrent tensor operations, which fully leverages the power of parallelization and GPU, and therefore is extremely efficient on large and densely connected constraint networks.

Abstract

We propose a new arc consistency enforcement paradigm that transforms arc consistency enforcement into recurrent tensor operations. In each iteration of the recurrence, all involved processes can be fully parallelized with tensor operations. And the number of iterations is quite small. Based on these benefits, the resulting algorithm fully leverages the power of parallelization and GPU, and therefore is extremely efficient on large and densely connected constraint networks.
Paper Structure (14 sections, 3 theorems, 4 equations, 3 figures, 1 table, 2 algorithms)

This paper contains 14 sections, 3 theorems, 4 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notation
  3. Recurrent Arc Consistency (RAC) Enforcement
  4. RAC Enforcement with Tensor Accelerating (RTAC)
  5. Experiments
  6. Configuration
  7. Benchmark
  8. Result
  9. Conclusion
  10. Proof of Lemma \ref{['lemma:1']}
  11. Proof of Proposition \ref{['prop:1']}
  12. Proof of Proposition \ref{['prop:2']}
  13. Pseudocode of Backtrack search
  14. Source Code of RTAC

Key Result

lemma thmcounterlemma

For any $(x,a)\in D$, if there exists $c_{xy}\in C_x$ and $D_{\widetilde{ac}}^{\prime}\subseteq D_{\widetilde{ac}}$ such that $c_{xy}|_{(x, a)}\subseteq D_{\widetilde{ac}}^{\prime}$, then $(x,a)\in D_{\widetilde{ac}}$.

Figures (3)

  • Figure 1: A variable $y$ is represented as a 1d array indexed by the values in $dom(y)$. In this array, $y[a]=1$ represents $y$ has the value $a$, and $y[a]=0$ represents not. Similarly, a constraint $C_{xy}$ is represented as a 2d array. $Sup_{xy}[a]$ represents the number of collected supports of $(x, a)$ on the constraint $C_{xy}$.
  • Figure 2: The illustration of arc consistency enforcement with tensor parallzation.
  • Figure 3: Running time (ms) of one assignment in backtrack search. The results are an average of 50K assignments.

Theorems & Definitions (6)

  • lemma thmcounterlemma
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proof
  • proof
  • proof