3-Dimensional Single Active Layer Routing
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Complexity of pairwise shortest path routing in the grid
Theoretical Computer Science
Routing vertex disjoint steiner-trees in a cubic grid and connections to VLSI
Discrete Applied Mathematics
Improved Algorithms for the 2-Vertex Disjoint Paths Problem
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Subgraphs generating algorithm for obtaining set of node-disjoint paths in terrain-based mesh graphs
MIG'10 Proceedings of the Third international conference on Motion in games
New solutions for disjoint paths in P systems
Natural Computing: an international journal
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A number of basic models for VLSI layout are based on the construction of node-disjoint paths between terminals on a multilayer grid. In this setting, one is interested in minimizing both the number of layers required and the area of the underlying grid. Building on work of Cutler and Shiloach [ Networks, 8 (1978), pp. 253--278], Aggarwal et al. [ Proc. 26th IEEE Symposium on Foundations of Computer Science , Portland, OR, 1985; Algorithmica, 6 (1991), pp. 241--255], and Aggarwal, Klawe, and Shor [ Algorithmica}, 6 (1991), pp. 129--151], we prove an upper-bound trade-off between these two quantities in a general multilayer grid model. As a special case of our main result, we obtain significantly improved bounds for the problem of routing a full permutation on the mesh using node-disjoint paths; our new bound here is within polylogarithmic factors of the bisection bound. Our algorithms involve some new techniques for analyzing the structure of node-disjoint paths in planar graphs and indicate some respects in which this problem, at least in the planar case, is fundamentally different from its edge-disjoint counterpart.