Multi-way partitioning using bi-partition heuristics

design automation conference, 2000, Pages 667-672.

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When the target graph is large, the hierarchical approach can have a cut cost which is about 77% better than the single-pass all-way bi-partition approach

Abstract:

The multi-way partition problem is very important in various applications. In this paper, we use analytical and experimental results to study the k-way partition problem. We introduce the concept of embedding graph for the the k-way partition problem. Based on this concept, we explain different scenarios of using a bi-partition heuristic ...More

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Introduction
  • Graph partitioning is an important problem and has extensive application to many areas in VLSI design [3].
  • The problem is to partition the vertices of a graph in IC into roughly equal parts, such that the number of edges connecting vertices in different parts is minimized.
  • To the presentation, the authors use a graph model.
  • A high quality graph partitioning algorithm greatly affects the feasibility, quality, and cost of the resulting system
Highlights
  • Graph partitioning is an important problem and has extensive application to many areas in VLSI design [3]
  • If the optimal cut cost for a k-way partition problem is C, we prove that the cut cost from the hierarchical approach has an upper bound of 6C log k while the cut cost from the all-way bi-partition approach has an upper bound of 6Ck where k is the number of partitions
  • We showed that the cut cost upper bound for the hierarchical bi-partition approach is O(6 log IC) of the optimal result and the cut cost upper bound for the allway bi-partition approach is O ( 6 k ) of the optimal result assuming that we are using a &approximation bi-partition heuristic
  • These two upper bounds suggests that the hierarchical approach is a better way t o solve the &way partition problem
  • When the target graph is large, the hierarchical approach can have a cut cost which is about 77% better than the single-pass all-way bi-partition approach
Methods
  • A is a direct extension of 2-way FM-like algorithms.
  • In the 2-way FM-like algorithms, each node can be moved to only one definite destination partition.
  • In the lc-way partition problem, each node has IC - 1 possible destination partitions.
  • Method A is based on the 2-way FM algorithm while allowing moving any node to any of the IC - 1 partitions.
  • Method B is a all-way bi-partition improvement.
  • It starts with an initial k-way
Results
  • THE HIERARCHICAL RESULTS USING THE ALL

    WAY ALGORITHM.

    Conference, pages 530-533. IEEE/ACM, 1997.

    [2] C.
Conclusion
  • The authors introduced the concept of embedding graph to theoretically analyze different IC-way partition algorithms.
  • The authors showed that the cut cost upper bound for the hierarchical bi-partition approach is O(6 log IC) of the optimal result and the cut cost upper bound for the allway bi-partition approach is O ( 6 k ) of the optimal result assuming that the authors are using a &approximation bi-partition heuristic.
  • The hierarchical approach produces 7.1%better results and is 144 times faster than the all-way approach
Summary
  • Introduction:

    Graph partitioning is an important problem and has extensive application to many areas in VLSI design [3].
  • The problem is to partition the vertices of a graph in IC into roughly equal parts, such that the number of edges connecting vertices in different parts is minimized.
  • To the presentation, the authors use a graph model.
  • A high quality graph partitioning algorithm greatly affects the feasibility, quality, and cost of the resulting system
  • Methods:

    A is a direct extension of 2-way FM-like algorithms.
  • In the 2-way FM-like algorithms, each node can be moved to only one definite destination partition.
  • In the lc-way partition problem, each node has IC - 1 possible destination partitions.
  • Method A is based on the 2-way FM algorithm while allowing moving any node to any of the IC - 1 partitions.
  • Method B is a all-way bi-partition improvement.
  • It starts with an initial k-way
  • Results:

    THE HIERARCHICAL RESULTS USING THE ALL

    WAY ALGORITHM.

    Conference, pages 530-533. IEEE/ACM, 1997.

    [2] C.
  • Conclusion:

    The authors introduced the concept of embedding graph to theoretically analyze different IC-way partition algorithms.
  • The authors showed that the cut cost upper bound for the hierarchical bi-partition approach is O(6 log IC) of the optimal result and the cut cost upper bound for the allway bi-partition approach is O ( 6 k ) of the optimal result assuming that the authors are using a &approximation bi-partition heuristic.
  • The hierarchical approach produces 7.1%better results and is 144 times faster than the all-way approach
Tables
  • Table1: SINGLE-PASASLL-WAY ALGORITHM vs. THE HIERARCHICAL ALGORITHM ( CONCLUSION: THE HIERARCHICAL APPROACH IS MORE
  • Table2: MULTI-PASSEXHAUSTIVE ALL-WAY ALGORITHM VS. GAIN-BASED
Download tables as Excel
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