Evaluation of ILP-based approaches for partitioning into colorful components

The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances

Fast branching algorithm for Cluster Vertex Deletion

In the family of clustering problems, we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hueffner et al. [Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant O(2^k * k^9 + n * m)-time fixed-parameter algorithm, parameterized by the solution size. In our work, we pick up this line of research and present an O(1.9102^k * (n + m))-time branching algorithm

Orientation-dependent C60 electronic structures revealed by photoemission

We observe, with angle-resolved photoemission, a dramatic change in the electronic structure of two C60 monolayers, deposited respectively on Ag (111) and (100) substrates, and similarly doped with potassium to half-filling of the C60 lowest unoccupied molecular orbital. The Fermi surface symmetry, the bandwidth, and the curvature of the dispersion at Gamma point are different. Orientations of the C60 molecules on the two substrates are known to be the main structural difference between the two monolayers, and we present new band-structure calculations for some of these orientations. We conclude that orientations play a key role in the electronic structure of fullerides.Comment: 4 pages, 4 figure

Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

The pi -> pi pi process in nuclei and the restoration of chiral symmetry

The results of an extensive campaign of measurements of the pi -> pi pi process in the nucleon and nuclei at intermediate energies are presented. The measurements were motivated by the study of strong pi pi correlations in nuclei. The analysis relies on the composite ratio C_{pi pi}^A, which accounts for the clear effect of the nuclear medium on the (pi pi) system. The comparison of the C_{pi pi}^A distributions for the (pi pi)_{I=J=0} and (pi pi)_{I=0,J=2} systems to the model predictions indicates that the C_{pi pi}^A behavior in proximity of the 2m_pi threshold is explainable through the partial restoration of chiral symmetry in nuclei.Comment: accepted for publication in Nucl. Phys.

Enumerating Isolated Cliques in Temporal Networks

Isolation is a concept from the world of clique enumeration that is mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we lift the isolation concept to this setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of fixed-parameter enumeration algorithms for five of these six clique types employing the parameter "degree of isolation". On the empirical side, we implement and test these algorithms on (temporal) social network data, obtaining encouraging preliminary results

Fixed-Parameter Algorithms in Analysis of Heuristics for Extracting Networks in Linear Programs

We consider the problem of extracting a maximum-size reflected network in a linear program. This problem has been studied before and a state-of-the-art SGA heuristic with two variations have been proposed. In this paper we apply a new approach to evaluate the quality of SGA\@. In particular, we solve majority of the instances in the testbed to optimality using a new fixed-parameter algorithm, i.e., an algorithm whose runtime is polynomial in the input size but exponential in terms of an additional parameter associated with the given problem. This analysis allows us to conclude that the the existing SGA heuristic, in fact, produces solutions of a very high quality and often reaches the optimal objective values. However, SGA contain two components which leave some space for improvement: building of a spanning tree and searching for an independent set in a graph. In the hope of obtaining even better heuristic, we tried to replace both of these components with some equivalent algorithms. We tried to use a fixed-parameter algorithm instead of a greedy one for searching of an independent set. But even the exact solution of this subproblem improved the whole heuristic insignificantly. Hence, the crucial part of SGA is building of a spanning tree. We tried three different algorithms, and it appears that the Depth-First search is clearly superior to the other ones in building of the spanning tree for SGA. Thereby, by application of fixed-parameter algorithms, we managed to check that the existing SGA heuristic is of a high quality and selected the component which required an improvement. This allowed us to intensify the research in a proper direction which yielded a superior variation of SGA

Towards Optimal and Expressive Kernelization for d-Hitting Set

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example, fault diagnosis, automatic program verification, and the noise-minimizing assignment of frequencies to radio transmitters. We show a linear-time algorithm that transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k^d) hyperedges and vertices. In terms of parameterized complexity, this is a problem kernel. Our kernelization algorithm is based on speeding up the well-known approach of finding and shrinking sunflowers in hypergraphs, which yields problem kernels with structural properties that we condense into the concept of expressive kernelization. We conduct experiments to show that our kernelization algorithm can kernelize instances with more than 10^7 hyperedges in less than five minutes. Finally, we show that the number of vertices in the problem kernel can be further reduced to O(k^{d-1}) with additional O(k^{1.5 d}) processing time by nontrivially combining the sunflower technique with d-Hitting Set problem kernels due to Abu-Khzam and Moser.Comment: This version gives corrected experimental results, adds additional figures, and more formally defines "expressive kernelization

Minimizing movement: Fixed-parameter tractability

We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network messages, etc.) to achieve a global property in the network while minimizing the maximum or average movement (expended energy). The only previous theoretical results about this class of problems are about approximation, and mainly negative: many movement problems of interest have polynomial inapproximability. Given that the number of mobile agents is typically much smaller than the complexity of the environment, we turn to fixed-parameter tractability. We characterize the boundary between tractable and intractable movement problems in a very general set up: it turns out the complexity of the problem fundamentally depends on the treewidth of the minimal configurations. Thus the complexity of a particular problem can be determined by answering a purely combinatorial question. Using our general tools, we determine the complexity of several concrete problems and fortunately show that many movement problems of interest can be solved efficiently.Hungarian Scientific Research Foundation (OTKA) (grant 67651