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Robust subgraphs for trees and paths

2006
*
ACM Transactions on Algorithms
*

In this paper we consider the problems of finding heavy

doi:10.1145/1150334.1150341
fatcat:aflsaxg2mrcz7gyf7znsfrrvaq
*paths**and*heavy*trees*of k edges. ... In addition, we consider variations in which the*subgraph*itself is restricted to be a*path*or a*tree*. ... We describe polynomial time algorithms*for*the problems of finding a*path*-*robust**path**and*a*tree*-*robust**tree*. ...##
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Robust Subgraphs for Trees and Paths
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we consider the problems of finding heavy

doi:10.1007/978-3-540-27810-8_6
fatcat:xbzebstt5bea5pcdjd7gx6tmz4
*paths**and*heavy*trees*of k edges. ... In addition, we consider variations in which the*subgraph*itself is restricted to be a*path*or a*tree*. ... We describe polynomial time algorithms*for*the problems of finding a*path*-*robust**path**and*a*tree*-*robust**tree*. ...##
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Biomolecular network motif counting and discovery by color coding

2008
*
Bioinformatics
*

In this article, we show how to apply the 'color coding' technique

doi:10.1093/bioinformatics/btn163
pmid:18586721
pmcid:PMC2718641
fatcat:eq2rjaqqzfapvdsaohuumlggtq
*for*counting non-induced occurrences of*subgraph*topologies in the form of*trees**and*bounded treewidth*subgraphs*. ... Yet no practical algorithm exists*for*counting non-induced occurrences, or counting*subgraphs*with k ≥ 8 vertices. ... al. (2007) ; Przulj et al. (2004)*for**subgraph*counting-provided that the query*subgraph*G is either a simple*path*, a*tree*or a bounded treewidth*subgraph*. ...##
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Robust minimum cost flow problem under consistent flow constraints

2021
*
Annals of operations research (2021). doi:10.1007/s10479-021-04426-0
*

In particular, the Integral Flow Theorem of Dantzig

doi:10.18154/rwth-2022-00487
fatcat:h3tvpx5bvzgolksykdqmpxxayq
*and*Fulkerson does not hold.*For*this reason, we require integral flows in the entire paper. ... The*robust*minimum cost flow problem under consistent flow constraints (RobMCF≡) is a new extension of the minimum cost flow (MCF) problem. ... Funding Open Access funding enabled*and*organized by Projekt DEAL. ...##
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Multicast 1+1 protection: The case for simple network coding

2015
*
2015 International Conference on Computing, Networking and Communications (ICNC)
*

In order to solve this problem, an optimal ILP

doi:10.1109/iccnc.2015.7069457
dblp:conf/iccnc/MohandespourK15
fatcat:rxmlltmj25bw7pfjhxjuy7eeom
*and*three efficient heuristic algorithms are proposed. ... Particularly, we show how to achieve instantaneous failure recovery*and*cost efficiency by allowing intermediate nodes to merge their incoming flows by a simple network code, i.e., logical OR operation ... In the following we describe necessary*and*sufficient conditions*for**subgraph*H. s,di is failed*and*p 2 s,di is not. ...##
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Fast Discovery of Reliable k-terminal Subgraphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

We present a novel

doi:10.1007/978-3-642-13672-6_17
fatcat:2vjia6zl7zg3rbtxd3gba7r3re
*and*efficient algorithm*for*solving the most reliable*subgraph*problem with multiple query nodes on undirected random graphs. ... Reliable*subgraphs*are useful*for*summarizing connectivity between given query nodes. Formally, we are given a graph G = (V, E), a set of query (or terminal) nodes Q ⊂ V ,*and*a positive integer B. ... We would like to thank the Biomine team*and*especially Lauri Eronen*for*providing the Biomine Crawler. ...##
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Robust Minimum Cost Flow Problem Under Consistent Flow Constraints
[article]

2020
*
arXiv
*
pre-print

In particular, the Integral Flow Theorem of Dantzig

arXiv:2008.02035v1
fatcat:efsxgf7az5duta7qgwa6zuva44
*and*Fulkerson does not hold.*For*this reason, we require integral flows in the entire paper. ... The*robust*minimum cost flow problem under consistent flow constraints (RobMCF≡) is a new extension of the minimum cost flow (MCF) problem. ... Due to the composition of digraph G, a shortest (o, q)-*path*p in*subgraph*G−A fix is composed of a shortest (o, w)-*path*p 1 in*subgraph*G 1 −A fix ,*and*a shortest (w, q)*path*p 2 in*subgraph*G 2 − A fix ...##
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Page 3027 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

If

*for*any vertex v #r of G there are k openly vertex-disjoint*paths*from r to v, then there are k independent spanning*trees*rooted at r in G.” ... Since minimum spanning*trees*depend on the realization of the edge costs, we define the*robust*spanning*tree*problem to hedge against the worst case contingency,*and*present a mixed integer programming ...##
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Cycle construction and geodesic cycles with application to the hypercube

2014
*
Ars Mathematica Contemporanea
*

*For*the hypercube graph, geodesic cycles are characterized,

*and*it is shown how hypercube geodesic cycles can be constructed in two steps from a special basis. ... investigated, where cycles from particular subsets (such as bases) are added together so that each partial sum is also a cycle or each new cycle intersects the sum of the preceding terms in a nontrivial

*path*... When G is a

*tree*, we can get a

*robustness*-related result. In the graph G × T , T a

*tree*, a cycle z contained in a

*subgraph*G × v

*for*some v ∈ V (T ) is called a level cycle. Proof. ...

##
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Fault-Tolerant Logical Network Structures

2016
*
Bulletin of the European Association for Theoretical Computer Science
*

As the vertices

dblp:journals/eatcs/Parter16
fatcat:b367phvhmbe7riq4qkixr26tsi
*and*edges of the network may occasionally fail or malfunction, it is desirable to make those structures*robust*against failures. ... In this survey, we review some recent results*for*designing FT network structures. ... I would also like to thank Mohsen Ghaffari*for*fruitful discussions*and**for*his great contribution in reviewing this survey. ...##
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Shortest-path metric approximation for random subgraphs

2006
*
Random structures & algorithms (Print)
*

The number of edges in Q is O(p −c n 1+2/c log n)

doi:10.1002/rsa.20150
fatcat:hu4fvapi3vfddbp7pfcwsersgu
*for*edge-induced random*subgraphs**and*O(p −2c n 1+2/c log 2 n)*for*vertexinduced random*subgraphs*, where n is the number of vertices in G, p the sampling ... We consider graph optimization problems where the cost of a solution depends only on the shortest-*path*metric in the graph, such as Steiner*Tree*or Traveling Salesman. ... In other words, we are not allowed to use*paths*in Q leaving the*subgraph*H. In fact, we construct a "*robust*spanner" which is resistant to random failure or vertices or edges. ...##
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Quantifying Systemic Evolutionary Changes by Color Coding Confidence-Scored PPI Networks
[chapter]

2009
*
Lecture Notes in Computer Science
*

Beyond the previously reported differences between unicellular

doi:10.1007/978-3-642-04241-6_4
fatcat:hgna3xph75dbriowohshroemfu
*and*multicellular organisms, we reveal major differences between prokaryotes*and*unicellular eukaryotes. ... This establishes,*for*the first time on a statistically sound data basis, that evolutionary distance can be monitored in terms of elevated systemic arrangements. ... As a result, we were able to reveal differences between uni-*and*multicellular as well as pro-*and*eukaryotic organisms. ...##
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Frequent pattern-growth approach for document organization

2008
*
Proceeding of the 2nd international workshop on Ontologies and nformation systems for the semantic web - ONISW '08
*

The similarity of the documents is measured in terms of the number of frequent

doi:10.1145/1458484.1458496
dblp:conf/cikm/AkbarA08
fatcat:4xz32abzyfe6do4rmalsslpkvi
*subgraphs*appearing in the corresponding document-graphs. ... We incorporate a graph mining approach with one of the well-known association rule mining procedures, FPgrowth, to discover the frequent*subgraphs*among the documentgraphs. ... Let β be a*subgraph**for*which a single*path*is generated by traversing the branches of the FP-*tree*ending with β. ...##
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Convex skeletons of complex networks

2018
*
Journal of the Royal Society Interface
*

A convex network can be defined as a network such that every connected induced

doi:10.1098/rsif.2018.0422
pmid:30111666
fatcat:j6owq6dpovfxdnkmd6bkvkrppe
*subgraph*includes all the shortest*paths*between its nodes. ... We present different approaches*for*extracting convex skeletons*and*apply them to social collaboration*and*protein interactions networks, autonomous systems graphs*and*food webs. ... of network convexity*and*convex skeletons, Michele Coscia*for*implementations of network backbones*and*Martin Rosvall*for*implementations of community detection algorithms. ...##
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On Finding Dense Subgraphs in Bipartite Graphs: Linear Algorithms
[article]

2018
*
arXiv
*
pre-print

We also demonstrate that the algorithms are

arXiv:1810.06809v3
fatcat:mbschco44nbfzg7zrec27pwwym
*robust*against deliberate camouflaging*and*other perturbations. ... We provide a novel algorithm S-*tree*,*and*its extension, S-forest, that solves the problem efficiently. ...*And*the depth of S-*tree*is bounded by Max(|I(m)|). IV. DENSE*SUBGRAPH*MINING WITH S-*TREE*Building upon the S-*tree*structure, we now introduce two algorithms*for*dense*subgraph*mining. ...
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