1. Network Modelling Group
An Overview of the Minimum-Congestion Hypergraph Embedding in a Cycle (MCHEC) Problem
By Yong Wang
Jun 4, 2002
2018/11/9
Network Modelling Group

2. Network Modelling Group
Road Map
Introduction to MCHEC
Some other variants of MCHEC
The previous research results
References
2018/11/9
Network Modelling Group

3. Network Modelling Group
Introduction
What is MCHEC ?
The MCHEC problem is to embed the hyperedges of the hypergraph as paths on a cycle with the same number of vertices, such that congestion (the maximum number of paths that use any single edge in the cycle) is minimized.
Electronic design automation
Parallel computing
Computer communication on a ring network
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4. MCHEC Problem Variants
Weighted/Unweighted & Hypergraph/Graph
Weighted Hypergraph Embedding(WHEC) (NP-Complete)
Weighted Graph Embedding(WGEC) (NP)
Unweighted Hypergraph Embedding(HEC) (NP)
Unweighted Graph Embedding(GEC) (P)
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5. Previous works – MCHEC (1)
NP Complete [1]
A linear approximation algorithm [1]
to compute an embedding whose congestion is at most three times optimal (i.e. 3-approximation)
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6. Previous works – MCHEC (2)
2-approximation algorithm 1 [3]
to transform the MCHEC problem to a LP
2-approximation algorithm 2 [3]
to solve the problem in linear time by transforming hyperedges to the normal edges
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7. Previous works – MCHEC (3)
A very simple 2-approximation algorithm [5]
runs in linear time
routes the hyperedges in the clockwise direction starting from the lowest numbered vertex to the highest numbered vertex.
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8. Network Modelling Group
Previous works - GEC
A simple version of MCHEC
For normal graph but not hypergraph, i.e. all hyperedges contain exactly only two vertices
Be solvable in polynomial time using a linear time algorithm, i.e. the GEC problem is in the class of P but not NP [6]
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9. Network Modelling Group
Previous works - WGEC
NP Complete [2]
Reducing PARTITION to DECISION-WGEC
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10. Network Modelling Group
Previous works - WHEC
NP Complete [2]
WGEC is a subproblem of WHEC &&
WGEC is NP complete
2 appro. algorithm 1: Formulated as ILP [2]
Get idea from [3]
LP-relaxation && Rounding heuristic
Disadvantage: Time Complexity is high, so …
2 appro. Algorithm 2: linear-time [2]
greedily remove the longest adjacent-path of each
hyperedge
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11. Network Modelling Group
References (1)
[1] J. L. Ganley and J. P. Cohoon, “Minimum-congestion
hypergraph embedding in a cycle”, IEEE Trans. Comput. 46
(5) (1997)
[2] SingLing Lee and Hann-Jang Ho, “Algorithms and
Complexity for Weighted Hypergraph Embedding in a Cycle",
[3] T. Gonzalez. “Improved approximation algorithms for
embedding hyperedges in a cycle", Information Processing
Letters 67 (4) (1998)
[4] J. L. Ganley and J. P. Cohoon, “A provably good moat routing
algorithm”, Proc. Sixth Grate lakes Symp. VLSI (1996)
86-91
[5] T. Carpenter, S. Cosares, J. L. Ganley and I. Saniee, “A
simple approximation algorithm for two problems in circuit
design”, IEEE Trans. Comput. 47 (11) (1998)
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12. Network Modelling Group
References (2)
[6] A. Frank, T. Nishizeki, N. Saito, H. Suzuki, E. Tardos, “Algorithms for routing around a rectangle”, Discrete Appl. Math. 40 (3) (1992)
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