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Multivariate Algorithmics for NPHard String Problems
, 2014
"... String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NPhard. This motivates the search for (fixedparameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NPha ..."
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String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NPhard. This motivates the search for (fixedparameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NPhard string problems and identify challenges for future research.
The Complexity of Degree Anonymization by Vertex Addition
, 2015
"... Motivated by applications in privacypreserving data publishing, we study the problem of making an undirected graph kanonymous by adding few vertices (together with some incident edges). That is, after adding these “dummy vertices”, for every vertex degree d appearing in the resulting graph, there ..."
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Motivated by applications in privacypreserving data publishing, we study the problem of making an undirected graph kanonymous by adding few vertices (together with some incident edges). That is, after adding these “dummy vertices”, for every vertex degree d appearing in the resulting graph, there shall be at least k vertices with degree d. We explore three variants of vertex addition (justified by realworld considerations) and study their (parameterized) computational complexity. We derive mostly intractability results, even for very restricted cases (including trees and boundeddegree graphs) but also obtain some encouraging fixedparameter tractability results.
On Explaining Integer Vectors by Few Homogenous Segments
, 2013
"... We extend previous studies on NPhard problems dealing with the decomposition of nonnegative integer vectors into sums of few homogeneous segments. These problems are motivated by radiation therapy and database applications. If the segments may have only positive integer entries, then the problem i ..."
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We extend previous studies on NPhard problems dealing with the decomposition of nonnegative integer vectors into sums of few homogeneous segments. These problems are motivated by radiation therapy and database applications. If the segments may have only positive integer entries, then the problem is called Vector Explanation +. If arbitrary integer entries are allowed in the decomposition, then the problem is called Vector Explanation. Considering several natural parameterizations (including maximum vector entry, maximum difference between consecutive vector entries, maximum segment length), we obtain a refined picture of the computational (in)tractability of these problems. In particular, we show that in relevant cases Vector Explanation + is algorithmically harder than Vector Explanation.
HIndex Manipulation by Merging Articles: Models, Theory, and Experiments
, 2015
"... An author’s profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the Hindex. The author is allowed to merge articles, which may affect the Hindex. We analyze the parameterized complexity of maximizing the Hindex using article merges. Here ..."
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An author’s profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the Hindex. The author is allowed to merge articles, which may affect the Hindex. We analyze the parameterized complexity of maximizing the Hindex using article merges. Herein, to model realistic manipulation scenarios, we define a compatability graph whose edges correspond to plausible merges. Moreover, we consider multiple possible measures for computing the citation count of a merged article. For the measure used by Google Scholar, we give an algorithm that maximizes the Hindex in linear time if the compatibility graph has constantsize connected components. In contrast, if we allow to merge arbitrary articles, then already increasing the Hindex by one is NPhard. Experiments on Google Scholar profiles of AI researchers show that the Hindex can be manipulated substantially only by merging articles with highly dissimilar titles, which would be easy to discover.
A Refined Complexity Analysis of Finding the Most Vital Edges for Undirected Shortest Paths
"... We study the NPhard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices s and t, the goal is to delete as few edges as possible in order to increase the length of the ..."
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We study the NPhard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices s and t, the goal is to delete as few edges as possible in order to increase the length of the (new) shortest stpath as much as possible. This scenario has been mostly studied from the viewpoint of approximation algorithms and heuristics, while we particularly introduce a parameterized and multivariate point of view. We derive refined tractability as well as hardness results, and identify numerous directions for future research. Among other things, we show that increasing the shortest path length by at least one is much easier than to increase it by at least two.
Uniform Kernelization Complexity of Hitting Forbidden Minors
"... The FMinorFree Deletion problem asks, for a fixed set F and an input consisting of a graph G and integer k, whether k vertices can be removed from G such that the resulting graph does not contain any member of F as a minor. It generalizes classic graph problems such as Vertex Cover and Feedback Ve ..."
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The FMinorFree Deletion problem asks, for a fixed set F and an input consisting of a graph G and integer k, whether k vertices can be removed from G such that the resulting graph does not contain any member of F as a minor. It generalizes classic graph problems such as Vertex Cover and Feedback Vertex Set. This paper analyzes to what extent provably effective and efficient preprocessing is possible for FMinorFree Deletion. Fomin et al. (FOCS 2012) showed that the special case Planar FMinorFree Deletion (when F contains at least one planar graph) has a kernel of polynomial size: instances (G, k) can efficiently be reduced to equivalent instances (G′, k) of size f(F) · kg(F) for some functions f and g. The degree g of the polynomial grows very quickly; it is not even known to be computable. Fomin et al. left open whether Planar FMinorFree Deletion has kernels whose size is uniformly polynomial, i.e., of the form f(F) ·kc for some universal constant c that does not depend on F. Our results in this paper are twofold. 1. We prove that not all Planar FMinorFree Deletion problems have uniformly polynomial kernels (unless NP ⊆ coNP/poly). Since a graph class has bounded treewidth