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- Robert J. Cimikowski
- Discrete Applied Mathematics
- 2002

- Robert J. Cimikowski, Paul Shope
- IEEE Trans. Neural Networks
- 1996

We present a neural-network algorithm for minimizing edge crossings in drawings of nonplanar graphs. This is an important subproblem encountered in graph layout. The algorithm finds either the minimum number of crossings or an approximation thereof and also provides a linear embedding realizing the number of crossings found. The parallel time complexity of… (More)

- Robert J. Cimikowski
- Inf. Sci.
- 1995

We present an empirical analysis of some heuristics for the graph thickness problem, i.e., decomposing a graph into the minimum number of planar subgraphs. The problem has applications in database systems, e.g., the layout of E-R diagrams. The heuristics are based on some algorithms for nding a maximal planar subgraph of a nonplanar graph. Empirical results… (More)

- Robert J. Cimikowski
- Pattern Recognition Letters
- 1992

Interconnection networks play a vital role in parallel computing architectures. We investigate topological properties of some networks proposed for parallel computation, based on their underlying graph models. The vertices of the graph correspond to processors and the edges represent communication links between processors. Parameters such as crossing number… (More)

- Minghui Jiang, Jianbo Qian, Zhongping Qin, Binhai Zhu, Robert J. Cimikowski
- Inf. Process. Lett.
- 2003

|We present a neural network algorithm for minimizing edge crossings in drawings of nonplanar graphs. This is an important subproblem encountered in graph layout. The algorithm nds either the minimum number of crossings or an approximation thereof and also provides a linear embedding realizing the number of crossings found. The parallel time complexity of… (More)

- Robert J. Cimikowski
- SODA
- 1995

We analyze several heuristics for finding a maximum planar subgraph of a nonplanar graph. The problem is NPhard, although heuristics which perform well in practice have been reported. In particular, we compare the two principle methods, based on path addition and vertex addition, respectively, with an incremental method, a “cycle packing” approach, and a… (More)

- Robert J. Cimikowski
- Inf. Process. Lett.
- 1990

- Robert J. Cimikowski, Brendan M Mumey
- Discrete Applied Mathematics
- 2007

We present a randomized polynomial-time approximation algorithm for the fixed linear crossing number problem (FLCNP). In this problem, the vertices of a graph are placed in a fixed order along a horizontal “node line” in the plane, each edge is drawn as an arc in one of the two half-planes (pages), and the objective is to minimize the number of edge… (More)