Hisao Tamaki

Optimal branch-decomposition of planar graphs in O ( n 3 ) Time

We give an <i>O</i>(<i>n</i>³) time algorithm for constructing a minimum-width branch-decomposition of a given planar graph with <i>n</i> vertices. This is achieved through a refinement to the previously best known algorithm of Seymour and Thomas, which runs in <i>O</i>(<i>n</i>⁴) time.

Optimal branch-decomposition of planar graphs in O(n 3 ) time

We give an O(n3) time algorithm for constructing a minimum-width branch-decomposition of a given planar graph with n vertices. This is achieved through a refinement to the previously best known algorithm of Seymour and Thomas, which runs in O(n4) time.

Computing directed pathwidth in O (1.89 n ) time

We give an algorithm for computing the directed pathwidth of a digraph with n vertices in O(1.89n) time. This is the first algorithm with running time better than the straightforward O*(2n). As a special case, it computes the pathwidth of an undirected graph in the same amount of time, improving on the algorithm due to Suchan and Villanger which runs in O(1.9657n) time.

Constant-Factor Approximations of Branch-Decomposition and Largest Grid Minor of Planar Graphs in O(n 1 + ε ) Time

We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let

A polynomial time algorithm for bounded directed pathwidth

{\mathop{\rm bw}}(G)

A Linear Time Heuristic for the Branch-Decomposition of Planar Graphs

be the branchwidth of G and

Improved Bounds on the Planar Branchwidth with Respect to the Largest Grid Minor Size

{\mathop{\rm gm}}(G)

A directed path-decomposition approach to exactly identifying attractors of boolean networks

the largest integer g such that G has a g×g grid as a minor. Let c ? 1 be a fixed integer and ?,β be arbitrary constants satisfying ?> c + 1.5 and β> 2c + 1.5. We give an algorithm which constructs in

A fast and simple subexponential fixed parameter algorithm for one-sided crossing minimization

O(n^{1+\frac{1}{c}}\log n)

Search Space Reduction through Commitments in Pathwidth Computation: An Experimental Study

time a branch-decomposition of G with width at most