Fixed-parameter algorithms for DAG Partitioning

Finding the origin of short phrases propagating through the web has been formalized by Leskovec et al. (2009) as DAG Partitioning: given an arc-weighted directed acyclic graph on n  vertices and m  arcs, delete arcs with total weight at most  k such that each resulting weakly-connected component con...

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Vydané v:Discrete Applied Mathematics Ročník 220; s. 134 - 160
Hlavní autori: van Bevern, René, Bredereck, Robert, Chopin, Morgan, Hartung, Sepp, Hüffner, Falk, Nichterlein, André, Suchý, Ondřej
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 31.03.2017
Elsevier BV
Predmet:
Algorithm engineering
Algorithms
Complement
Computer simulation
Data reduction
Evaluating heuristics
Graph algorithms
Graph theory
Graphs
Heuristic
Linear equations
Linear-time algorithms
Lower bounds
Multiway cut
NP-hard problem
Optimization
Partitioning
Polynomial-time data reduction
Run time (computers)
Studies
Trees (mathematics)
Evaluating heuristics
NP-hard problem
Algorithm engineering
Multiway cut
Graph algorithms
Linear-time algorithms
Polynomial-time data reduction
ISSN:0166-218X, 1872-6771
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Shrnutí:Finding the origin of short phrases propagating through the web has been formalized by Leskovec et al. (2009) as DAG Partitioning: given an arc-weighted directed acyclic graph on n  vertices and m  arcs, delete arcs with total weight at most  k such that each resulting weakly-connected component contains exactly one sink—a vertex without outgoing arcs. DAG Partitioning is NP-hard. We show an algorithm to solve DAG Partitioning in O(2k⋅(n+m))  time, that is, in linear time for fixed  k. We complement it with linear-time executable data reduction rules. Our experiments show that, in combination, they can optimally solve DAG Partitioning on simulated citation networks within five minutes for k≤190 and m being  107 and larger. We use our obtained optimal solutions to evaluate the solution quality of Leskovec et al.’s heuristic. We show that Leskovec et al.’s heuristic works optimally on trees and generalize this result by showing that DAG Partitioning is solvable in 2O(t2)⋅n time if a width-t tree decomposition of the input graph is given. Thus, we improve an algorithm and answer an open question of Alamdari and Mehrabian (2012). We complement our algorithms by lower bounds on the running time of exact algorithms and on the effectivity of data reduction.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.12.002