Polynomial time algorithms for the min cut problem on degree restricted trees
SIAM Journal on Computing
A polynomial algorithm for the min-cut linear arrangement of trees
Journal of the ACM (JACM)
Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On minimizing width in linear layouts
Discrete Applied Mathematics
Cluster analysis for hypertext systems
SIGIR '93 Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval
Dynamic Programming Treatment of the Travelling Salesman Problem
Journal of the ACM (JACM)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
SIAM Journal on Computing
Approximating layout problems on random geometric graphs
Journal of Algorithms
A Polyhedral Approach to Planar Augmentation and Related Problems
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
Fixed-parameter algorithms for protein similarity search under mRNA structure constraints
Journal of Discrete Algorithms
Cutwidth of Split Graphs, Threshold Graphs, and Proper Interval Graphs
Graph-Theoretic Concepts in Computer Science
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Computing Pathwidth Faster Than 2n
Parameterized and Exact Computation
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Computing the cutwidth of bipartite permutation graphs in linear time
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
TREEWIDTH and PATHWIDTH parameterized by the vertex cover number
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
Maximum common induced subgraph parameterized by vertex cover
Information Processing Letters
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We study the Cutwidth problem, where input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices. We give an algorithm for Cutwidth with running time O(2knO(1)). Here k is the size of a minimum vertex cover of the input graph G, and n is the number of vertices in G. Our algorithm gives an O(2n/2nO(1)) time algorithm for Cutwidth on bipartite graphs as a corollary. This is the first non-trivial exact exponential time algorithm for Cutwidth on a graph class where the problem remains NP-complete. Additionally, we show that Cutwidth parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless NP ⊆ coNP/poly. Our kernelization lower bound contrasts the recent result of Bodlaender et al.[ICALP 2011] that Treewidth parameterized by vertex cover does admit a polynomial kernel.