Journal of the ACM (JACM)
On algorithmic applications of the immersion order
Discrete Mathematics - Special issue on Graph theory
Dynamic Programming Treatment of the Travelling Salesman Problem
Journal of the ACM (JACM)
Introduction to Algorithms
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Machine Learning
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Almost 2-SAT Is Fixed-Parameter Tractable (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Correlation clustering with noisy input
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Generalized graph clustering: recognizing (p, q)-cluster graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
An improved parameterized algorithm for the minimum node multiway cut problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parameterized Complexity
Fixed-parameter tractability of directed multiway cut parameterized by the size of the cutset
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Important separators and parameterized algorithms
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
FPT suspects and tough customers: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Fixed-parameter tractability of multicut in directed acyclic graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We study a family of graph clustering problems where each cluster has to satisfy a certain local requirement. Formally, let µ be a function on the subsets of vertices of a graph G. In the (µ, p, q)- Partition problem, the task is to find a partition of the vertices into clusters where each cluster C satisfies the requirements that (1) at most q edges leave C and (2) µ(C) ≤ p. Our first result shows that if µ is an arbitrary polynomial-time computable monotone function, then (µ, p, q)- Partition can be solved in time nO(q), i.e., it is polynomial-time solvable for every fixed q. We study in detail three concrete functions µ (number of nonedges in the cluster, maximum number of non-neighbours a vertex has in the cluster, the number of vertices in the cluster), which correspond to natural clustering problems. For these functions, we show that (µ, p, q)-Partition can be solved in time 2O(p) ċ nO(1) and in randomized time 2O(q) ċ nO(1), i.e., the problem is fixed-parameter tractable parameterized by p or by q.