Given: A graph with 2n nodes where each node has the same weight. Goal: A partition (division) of the graph into two disjoint subsets A and B with minimum cut cost and |A| = |B| = n. where Ec(v) is the set of v’s incident edges that are cut by the cut line, and Enc(v) is the set of v’s incident edges that are not cut by the cut line.

We have developed two k-way bounded partitioning algorithms; one is evolutionary-based, while the other is a hierarchical graph center-based approach. The algorithms are implemented and compared with known partitioning algorithms.

Perform EIG partitioning and minimize ratio cut cost. Clique-based graph model: dotted edge has weight of 0.5, and solid edge with no label has weight of 0.25. {(a,f,d,g,i), (j,b,h,e,c)} is well-balanced and has low RC cost.

The tutorial introduces the partitioning with applications to VLSI circuit designs. The problem formulations include two-way, multiway, and multi-level partitioning, partitioning with replication, and performance driven partitioning. We depict the models of multiple pin nets for the partitioning processes. To derive the optimum

Give a good analysis and insight on graph partitioning algorithm based on the presented comparison. If we want to partition G(N,E), but it is too big to do efficiently, what can we do? What if Gc still too big? Refine edge cut (we have more degrees of freedom!) We have good initial partition from the uncoarsened graph. (so multiple trials!)

VLSI Physical Design: From Graph Partitioning to Timing Closure Chapter 8: Timing Closure 16 ©KLMH Lienig • Establish timing budgets for nets − Gate and wire delays must be optimized during timing driven layout design − Wire delays depend on wire lengths − Wire lengths are not known until after placement and routing

In this thesis, we present a polynomial time approximation algorithm for the global routing problem based on an integer programming formulation. The algorithm features a theoretical approximation bound, while ensuring all the routing demands are concurrently satisfied.

First performance-driven tools and parallel optimization algorithms for layout; better understanding of underlying theory (graph theory, solution complexity, etc.). 1985 -1990 More advanced tools for ICs and PCBs, with more sophisticated algorithms. 1975 -1985 Layout editors, e.g., place and route tools, first developed for printed circuit boards.

Tree partitioning problem is a special case of graph partitioning. A general graph partitioning though fast, is inefficient while partitioning a tree structure. An algorithm for tree partitioning that can handle large trees with less memory/run time requirement will …

Cite this Research Publication : Dr. Somasundaram K., “Graph Partitioning Algorithms in VLSI Design and Testing: Review”, in Proceeding of Discrete Mathematics and its Applications, 162-168, 2004.