
A heuristic use of dynamic programming to upperbound treewidth
For a graph G, let Ξ©(G) denote the set of all potential maximal cliques ...
read it

A polynomial time algorithm to compute the connected treewidth of a seriesparallel graph
It is well known that the treewidth of a graph G corresponds to the node...
read it

Fast FPTApproximation of Branchwidth
Branchwidth determines how graphs, and more generally, arbitrary connect...
read it

Spectral and Combinatorial Properties of Some Algebraically Defined Graphs
Let k> 3 be an integer, q be a prime power, and F_q denote the field of ...
read it

Finegrained complexity of graph homomorphism problem for boundedtreewidth graphs
For graphs G and H, a homomorphism from G to H is an edgepreserving map...
read it

Fast Algorithms for Join Operations on Tree Decompositions
Treewidth is a measure of how treelike a graph is. It has many importan...
read it

On Minrank and Forbidden Subgraphs
The minrank over a field F of a graph G on the vertex set {1,2,...,n} is...
read it
Efficient diagonalization of symmetric matrices associated with graphs of small treewidth
Let M=(m_ij) be a symmetric matrix of order n whose elements lie in an arbitrary field π½, and let G be the graph with vertex set {1,β¦,n} such that distinct vertices i and j are adjacent if and only if m_ijβ 0. We introduce a dynamic programming algorithm that finds a diagonal matrix that is congruent to M. If G is given with a tree decomposition π― of width k, then this can be done in time O(kπ― + k^2 n), where π― denotes the number of nodes in π―. Among other things, this allows one to compute the determinant, the rank and the inertia of a symmetric matrix in time O(kπ― + k^2 n).
READ FULL TEXT
Comments
There are no comments yet.