P. Mutzel and R. Weiskircher, Two-layer planarization in graph drawing. In K. Y. Chwa and O. H. Ibarra, eds., Proc. 9th Internat. Symp. on Algorithms and Computation (ISAAC '98), vol. 1533 of Lecture Notes in Comput. Sci., pp. 69-78, Springer, 1998. Home/Search Document Details and Download
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On the Parameterized Complexity of Layered Graph Drawing - Dujmovic, Fellows.. (2001) (6 citations) (Correct)
.... [HK99,JLM98] and if so, to produce such a drawing with straight line segments [JL99] even for edges which span multiple layers [EFL97] Integer linear programmingformulations have been developed for crossing minimization in layered graphs [HK99,JLMO98,JM97] and for 2 layer planarization [Mut97,MW98] The special case of two layers is important for the layer by layer sweep approach. Junger and Mutzel [JM97] summarize the many heuristics for 2 layer crossing minimization. Our companion paper [DFH ] addresses the 2 layer case. The remainder of this paper is organized as follows. Section 2 ....
P. Mutzel and R. Weiskircher. Two-layer planarization in graph drawing. In K. Y. Chwa and O. H. Ibarra, editors, Proc. 9th International Symposium on Algorithms and Computation (ISAAC'98), volume 1533 of Lecture Notes in Comput. Sci., pages 69-78. Springer, 1998.
A Fixed-Parameter Approach to Two-Layer Planarization - Dujmovic, Fellows.. (2001) (Correct)
....Planarization problem is NP complete even for graphs with only degree 1 vertices in the xed layer and vertices of degree at most 2 in the other layer [5] i.e. for collections of 1 and 2 paths. With the order of the vertices in both layers xed the problem can be solved in polynomial time [5, 14]. Integer linear programming algorithms have been presented for 1 and 2Layer Crossing Minimization [9, 18] J unger and Mutzel [9] survey numerous heuristics proposed for both problems, and experimentally compare their performance with the optimal solutions. They report that the iterated ....
....of O(log n) for a wide class of n vertex graphs. Despite the practical signi cance of the problems, 1 and 2 Layer Planarization have received less attention in the graph drawing literature than their crossing minimization counterparts. Integer linear programming algorithms have been presented [12, 14]. For acyclic graphs G, Shahrokhi et al. 15] present an O(n) time dynamic programming algorithm for 2 Layer Planarization of weighted acyclic graphs, for which the objective is to minimize the total weight of deleted edges. 1.1 Fixed Parameter Tractability and Our Results When the maximum ....
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P. Mutzel and R. Weiskircher. Two-layer planarization in graph drawing. In K. Y. Chwa and O. H. Ibarra, editors, Proc. 9th International Symp. on Algorithms and Computation (ISAAC'98), volume 1533 of Lecture Notes in Comput. Sci., pages 69-78. Springer, 1998.
A Fixed-Parameter Approach to Two-Layer Planarization - Dujmovic, Fellows.. (2004) (Correct)
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P. Mutzel and R. Weiskircher, Two-layer planarization in graph drawing. In K. Y. Chwa and O. H. Ibarra, eds., Proc. 9th Internat. Symp. on Algorithms and Computation (ISAAC '98), vol. 1533 of Lecture Notes in Comput. Sci., pp. 69-78, Springer, 1998.
The ABACUS System for Branch-and-Cut-and-Price Algorithms in.. - Jünger, Thienel (1998) (Correct)
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Petra Mutzel and Rene Weiskircher, `Two layer planarization in graph drawing', K.Y. Chwa and O.H. Ibarra (eds.) Proc. ISAAC '98, LNCS 1533, Springer Verlag, 1998, pp. 69--78.
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