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Известия ТРТУ
Тематический выпуск
УДК 681.3.06
Alexander Marchenko and Eldar Ulukhanov GRAPH PARTITIONING ALGORITHM BASED ON ADAPTIVE AUTOMATA
Hypergraph partitioning is an important problem and has extensive application in many areas. One of using of hypergraph partitioning is one step in VLSI physical design. Number of transistors in VLSI may exceed some millions. Therefore during design the routines like placement and routing cannot be handled due to complexity of known algorithm and memory limitation. The solution of this problem is using partitioning as a first step in physical design.
Partitioning is a complex problem which is NP-complete. There are a number of heuristic algorithm: GPLA[1], Kernigan-Lin[2] but due to NP-completeness they don’t find optimal solution in reasonable time. The best known approach is hMetis [3] - multilevel partitioning algorithm.
In this paper we propose an algorithm that partitions hypergraph into two parts. Multiway hypergraph partition provides due to bipartitioning in hierarchical manner. The approach of the bipartition comprises the following steps which can be repeated iteratively:
♦ Assign each node to a single adaptive automata.
♦ Reward or penalty each automata.
♦ Repeat step 2 if exit condition is not completed.
♦ Build partition using the states of automata.
The result of the algorithm is a number of subgraphs. A goal function is hyperedge cut - the number of the hyperedges that belong to the cut.
Additional metrics were calculated to appreciate the quality of the partition in comparison with hMetis:
♦ Sum of External Degrees is defined as a number of hyperedges that are incident but not fully inside this partition;
♦ Scaled cost and Absorption that were calculated in accordance with [3].
Testing shows that described approach provides competitive with hMetis results.
LITERATURE
1. B. John Oomen and Edward V. de St. Croix “Graph Partition Using Learning Automata“ IEEE transaction on computers, vol. 45, No 2, February 1996.
2. B.W. Kernigan and S.Lin, “An efficient heuristic procedure for partitioning graph”, Bell Syst. tech. J., vol.49, pp.291-307, Feb. 1970.
3. G.Karypis and V.Kumar, “Multilevel k-way hypergraph partitioning“, in Proc. IEEE- ACM Design Automation Conf., 1999, pp. 343-348.
