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Multilayer networks
 TOOL FOR MULTILAYER ANALYSIS AND VISUALIZATION OF NETWORKS 17 OF 18
, 2014
"... In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is impo ..."
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Cited by 34 (7 self)
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In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such “multilayer” features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize “traditional ” network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary
Embedding large subgraphs into dense graphs
, 2009
"... What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac’s theorem on Hamilton cycles and Tutte’s theorem on perfect matchings. Perfect matchings are generalized by perfect Fpackings, where instead of covering ..."
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Cited by 32 (11 self)
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What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac’s theorem on Hamilton cycles and Tutte’s theorem on perfect matchings. Perfect matchings are generalized by perfect Fpackings, where instead of covering all the vertices of G by disjoint edges, we want to cover G by disjoint copies of a (small) graph F. It is unlikely that there is a characterization of all graphs G which contain a perfect Fpacking, so as in the case of Dirac’s theorem it makes sense to study conditions on the minimum degree of G which guarantee a perfect Fpacking. The Regularity lemma of Szemerédi and the Blowup lemma of Komlós, Sárközy and Szemerédi have proved to be powerful tools in attacking such problems and quite recently, several longstanding problems and conjectures in the area have been solved using these. In this survey, we give an outline of recent progress (with our main emphasis on Fpackings, Hamiltonicity problems and tree embeddings) and describe some of the methods involved.
Repairing Multiple Failures with Coordinated and Adaptive Regenerating Codes
 in NetCod’2011: The 2011 International Symposium on Network Coding
, 2011
"... Abstract—Erasure correcting codes are widely used to ensure data persistence in distributed storage systems. This paper addresses the repair of such codes in the presence of simultaneous failures. It is crucial to maintain the required redundancy over time to prevent permanent data losses. We go bey ..."
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Cited by 30 (4 self)
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Abstract—Erasure correcting codes are widely used to ensure data persistence in distributed storage systems. This paper addresses the repair of such codes in the presence of simultaneous failures. It is crucial to maintain the required redundancy over time to prevent permanent data losses. We go beyond existing work (i.e., regenerating codes by Dimakis et al.) and propose coordinated regenerating codes allowing devices to coordinate during simultaneous repairs thus reducing the costs further. We provide closed form expressions of the communication costs of our new codes depending on the number of live devices and the number of devices being repaired. We prove that deliberately delaying repairs does not bring additional gains in itself. This means that regenerating codes are optimal as long as each failure can be repaired before a second one occurs. Yet, when multiple failures are detected simultaneously, we prove that our coordinated regenerating codes are optimal and outperform uncoordinated repairs (with respect to communication and storage costs). Finally, we define adaptive regenerating codes that selfadapt to the system state and prove they are optimal. Keywords—erasure correcting codes, regenerating codes, distributed storage, repair, multiple failures I.
Adding Regular Expressions to Graph Reachability and Pattern Queries
 Frontiers of Computer Science
, 2012
"... Abstract—It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressin ..."
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Cited by 30 (6 self)
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Abstract—It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity in a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubictime algorithms for evaluating graph pattern queries based on extended graph simulation, as opposed to the NPcompleteness of graph pattern matching via subgraph isomorphism. (4) The effectiveness, efficiency and scalability of these algorithms are experimentally verified using reallife data and synthetic data. I.
Parameterized algorithms for feedback set problems and their duals in tournaments
 Theoretical Computer Science
, 2006
"... The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournamen ..."
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Cited by 26 (8 self)
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The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions. We also address the parametric dual problems which are also natural optimization problems. We show that they are fixed parameter tractable not just in tournaments but in oriented directed graphs (where there is at most one directed arc between a pair of vertices). More specifically, the dual problem we show fixed parameter tractable are: Given an oriented directed graph, is there a subset of k vertices (arcs) that forms an acyclic directed subgraph of the graph? Our main results include: • an O((2.4143) k n ω) 1 algorithm for weighted feedback vertex set problem, and an O((2.415) k n ω) algorithm for weighted feedback arc set problem in tournaments; • an O((e2 k /k) k k 2 + min{m lg n,n 2}) algorithm for the dual of feedback vertex set problem (maximum vertex induced acyclic graph) in oriented directed graphs, and an O(4 k k +m) algorithm for the dual of feedback arc set problem (maximum arc induced acyclic graph) in general directed graphs. We also show that the dual of feedback vertex set is W[1]−hard in general directed graphs and the feedback arc set problem is fixed parameter tractable in dense directed graphs. Our results are the first non trivial results for these problems. Key words: tournaments, feedback vertex set, feedback arc set, parameterized complexity 1 ω is the exponent of the best matrix multiplication algorithm. Preprint submitted to Elsevier Science 12 May 2005 1
Hybrids in Real Time
, 2006
"... We describe some new and recent results that allow for the analysis and representation of reticulate evolution by nontree networks. In particular, we (1) present a simple result to show that, despite the presence of reticulation, there is always a welldefined underlying tree that corresponds to t ..."
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Cited by 24 (6 self)
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We describe some new and recent results that allow for the analysis and representation of reticulate evolution by nontree networks. In particular, we (1) present a simple result to show that, despite the presence of reticulation, there is always a welldefined underlying tree that corresponds to those parts of life that do not have a history of reticulation; (2) describe and apply new theory for determining the smallest number of hybridization events required to explain conflicting gene trees; and (3) present a new algorithm to determine whether an arbitrary rooted network can be realized by contemporaneous reticulation events. We illustrate these results with examples.
FixedParameter Tractability Results for Feedback Set Problems in Tournaments
 JOURNAL OF DISCRETE ALGORITHMS
, 2009
"... Complementing recent progress on classical complexity and polynomialtime approximability of feedback set problems in (bipartite) tournaments, we extend and improve fixedparameter tractability results for these problems. We show that Feedback Vertex Set in tournaments (FVST) is amenable to the nove ..."
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Cited by 23 (6 self)
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Complementing recent progress on classical complexity and polynomialtime approximability of feedback set problems in (bipartite) tournaments, we extend and improve fixedparameter tractability results for these problems. We show that Feedback Vertex Set in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depthbounded search tree for Feedback Arc Set in bipartite tournaments based on a new forbidden subgraph characterization. Moreover, we apply the iterative compression technique to dHitting Set, which generalizes Feedback Vertex Set in tournaments, and obtain improved upper bounds for the time needed to solve 4Hitting Set and 5Hitting Set. Using our parameterized algorithm for Feedback Vertex Set in tournaments, we also give an exact (not parameterized) algorithm for it running in O(1.709 n) time, where n is the number of input graph vertices, answering a question of Woeginger [Discrete Appl. Math. 156(3):397–405, 2008].
An exact minimum degree condition for Hamilton cycles in oriented graphs
"... We show that every sufficiently large oriented graph G with δ + (G), δ − (G) ≥ ..."
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Cited by 22 (12 self)
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We show that every sufficiently large oriented graph G with δ + (G), δ − (G) ≥
TDM VirtualCircuit Configuration for NetworkonChip
 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION SYSTEMS
, 2007
"... ... Multiplexing (TDM) Virtual Circuits (VCs) have been proposed to satisfy the QualityofService requirements of applications. TDM VC is a connectionoriented communication service by which two or more connections take turns to share buffers and link bandwidth using dedicated time slots. In the pa ..."
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Cited by 21 (6 self)
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... Multiplexing (TDM) Virtual Circuits (VCs) have been proposed to satisfy the QualityofService requirements of applications. TDM VC is a connectionoriented communication service by which two or more connections take turns to share buffers and link bandwidth using dedicated time slots. In the paper, we first give a formulation of the multinode VC configuration problem for arbitrary NoC topologies. A multinode VC allows multiple source and destination nodes on it. Then we address the two problems of path selection and slot allocation for TDM VC configuration. For the path selection, we use a backtracking algorithm to explore the path diversity, constructively searching the solution space. In the slot allocation phase, overlapped VCs must be configured such that no conflict occurs and their bandwidth requirements are satisfied. We define the concept of a logical network (LN) as an infinite set of associated (time slot, buffer) pairs with respect to a buffer on a given VC. Based on this concept, we develop and prove theorems that constitute sufficient and necessary conditions to establish conflictfree VCs. They are applicable for networks where all nodes operate with the same clock frequency but allowing different phases. Using these theorems, slot allocation for VCs is a procedure of assigning VCs to different LNs. TDM VC configuration can thus be predictable and correctbyconstruction. Our experiments on synthetic and real applications validate the effectiveness and efficiency of our approach.