Integer plane multiflows with a fixed number of demands
Journal of Combinatorial Theory Series B
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
#3-Regular bipartite planar vertex cover is #p-complete
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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We give a randomized algorithm for maximum edge-disjoint paths problem (MEDP) and the minimal total length of MEDP, if the graphs are planar and all terminals lie on the outer face in the order s1, s2,... sk, tk, tk-1,...t1. Moreover, if the degree of the graph is bounded by 3, the algorithm becomes deterministic and can also output the number of optimal solutions. On the other hand, we prove that the counting version of these problems are #P-hard even if restricted to planar graphs with maximum degree 3.