Inclusion and exclusion algorithm for the Hamiltonian Path Problem
Information Processing Letters
The vertex separation and search number of a graph
Information and Computation
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Partitioning graphs into connected parts
Theoretical Computer Science
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
A new characterization of P6-free graphs
Discrete Applied Mathematics
Removing local extrema from imprecise terrains
Computational Geometry: Theory and Applications
Dynamic programming meets the principle of inclusion and exclusion
Operations Research Letters
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 5.23 |
Suppose a graph G is given with two vertex-disjoint sets of vertices Z"1 and Z"2. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z"1 and Z"2, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of n-vertex graphs G=(V,E) in which Z"1 and Z"2 each contain a connected set that dominates all vertices in V@?(Z"1@?Z"2). We present an O^*(1.2051^n) time algorithm that solves it for this graph class. As a consequence, we can also solve this problem in O^*(1.2051^n) time for the classes of n-vertex P"6-free graphs and split graphs. This is an improvement upon a recent O^*(1.5790^n) time algorithm for these two classes. Our approach translates the problem to a generalized version of hypergraph 2-coloring and combines inclusion/exclusion with measure and conquer.