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Robust subgraphs for trees and paths

Refael Hassin, Danny Segev
2006 ACM Transactions on Algorithms  
In this paper we consider the problems of finding heavy 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.  ... 
doi:10.1145/1150334.1150341 fatcat:aflsaxg2mrcz7gyf7znsfrrvaq

Robust Subgraphs for Trees and Paths [chapter]

Refael Hassin, Danny Segev
2004 Lecture Notes in Computer Science  
In this paper we consider the problems of finding heavy 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.  ... 
doi:10.1007/978-3-540-27810-8_6 fatcat:xbzebstt5bea5pcdjd7gx6tmz4

Biomolecular network motif counting and discovery by color coding

N. Alon, P. Dao, I. Hajirasouliha, F. Hormozdiari, S. C. Sahinalp
2008 Bioinformatics  
In this article, we show how to apply the 'color coding' technique 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.  ... 
doi:10.1093/bioinformatics/btn163 pmid:18586721 pmcid:PMC2718641 fatcat:eq2rjaqqzfapvdsaohuumlggtq

Robust minimum cost flow problem under consistent flow constraints

Christina Maria Katharina Büsing, Arie Marinus Koster, Sabrina Schmitz
2021 Annals of operations research (2021). doi:10.1007/s10479-021-04426-0  
In particular, the Integral Flow Theorem of Dantzig 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.  ... 
doi:10.18154/rwth-2022-00487 fatcat:h3tvpx5bvzgolksykdqmpxxayq

Multicast 1+1 protection: The case for simple network coding

Mirzad Mohandespour, Ahmed E. Kamal
2015 2015 International Conference on Computing, Networking and Communications (ICNC)  
In order to solve this problem, an optimal ILP 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.  ... 
doi:10.1109/iccnc.2015.7069457 dblp:conf/iccnc/MohandespourK15 fatcat:rxmlltmj25bw7pfjhxjuy7eeom

Fast Discovery of Reliable k-terminal Subgraphs [chapter]

Melissa Kasari, Hannu Toivonen, Petteri Hintsanen
2010 Lecture Notes in Computer Science  
We present a novel 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.  ... 
doi:10.1007/978-3-642-13672-6_17 fatcat:2vjia6zl7zg3rbtxd3gba7r3re

Robust Minimum Cost Flow Problem Under Consistent Flow Constraints [article]

Christina Büsing and Arie M.C.A. Koster and Sabrina Schmitz
2020 arXiv   pre-print
In particular, the Integral Flow Theorem of Dantzig 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  ... 
arXiv:2008.02035v1 fatcat:efsxgf7az5duta7qgwa6zuva44

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  ... 

Cycle construction and geodesic cycles with application to the hypercube

Paul C. Kainen
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.  ... 
doi:10.26493/1855-3974.450.0b6 fatcat:xxrr4gsrengfzfskfkeo3k4zge

Fault-Tolerant Logical Network Structures

Merav Parter
2016 Bulletin of the European Association for Theoretical Computer Science  
As the vertices 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.  ... 
dblp:journals/eatcs/Parter16 fatcat:b367phvhmbe7riq4qkixr26tsi

Shortest-path metric approximation for random subgraphs

Jan Vondrák
2006 Random structures & algorithms (Print)  
The number of edges in Q is O(p −c n 1+2/c log n) 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.  ... 
doi:10.1002/rsa.20150 fatcat:hu4fvapi3vfddbp7pfcwsersgu

Quantifying Systemic Evolutionary Changes by Color Coding Confidence-Scored PPI Networks [chapter]

Phuong Dao, Alexander Schönhuth, Fereydoun Hormozdiari, Iman Hajirasouliha, S. Cenk Sahinalp, Martin Ester
2009 Lecture Notes in Computer Science  
Beyond the previously reported differences between unicellular 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.  ... 
doi:10.1007/978-3-642-04241-6_4 fatcat:hgna3xph75dbriowohshroemfu

Frequent pattern-growth approach for document organization

Monika Akbar, Rafal A. Angryk
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 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.  ... 
doi:10.1145/1458484.1458496 dblp:conf/cikm/AkbarA08 fatcat:4xz32abzyfe6do4rmalsslpkvi

Convex skeletons of complex networks

Lovro Šubelj
2018 Journal of the Royal Society Interface  
A convex network can be defined as a network such that every connected induced 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.  ... 
doi:10.1098/rsif.2018.0422 pmid:30111666 fatcat:j6owq6dpovfxdnkmd6bkvkrppe

On Finding Dense Subgraphs in Bipartite Graphs: Linear Algorithms [article]

Yikun Ban
2018 arXiv   pre-print
We also demonstrate that the algorithms are 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.  ... 
arXiv:1810.06809v3 fatcat:mbschco44nbfzg7zrec27pwwym
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