Regular Article: On the Complexity of DNA Physical Mapping
Advances in Applied Mathematics
Simple linear time recognition of unit interval graphs
Information Processing Letters
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs
Discrete Applied Mathematics
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
On problems without polynomial kernels
Journal of Computer and System Sciences
Interval Completion Is Fixed Parameter Tractable
SIAM Journal on Computing
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Two Edge Modification Problems without Polynomial Kernels
Parameterized and Exact Computation
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
Problem kernels for NP-complete edge deletion problems: split and related graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Polynomial kernels for 3-leaf power graph modification problems
Discrete Applied Mathematics
A 2k Kernel for the cluster editing problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Survey: A survey of the algorithmic aspects of modular decomposition
Computer Science Review
Parameterized Complexity
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Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (VxV)@?E such that the graph H=(V,E@?F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research. This problem is known to be FPT (Kaplan, Tarjan and Shamir, FOCS@?94), but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with O(k^3) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem, admits a kernel with O(k^2) vertices, completing a previous result of Guo (ISAAC@?07).