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Complexity of Cycle Length Modularity Problems in Graphs [article]

Edith Hemaspaandra, Holger Spakowski, Mayur Thakur
2003 arXiv   pre-print
In this paper, we study the computational complexity of cycle length modularity problems.  ...  Roughly speaking, in a cycle length modularity problem, given an input (undirected or directed) graph, one has to determine whether the graph has a cycle C of a specific length (or one of several different  ...  Cycle Length Modularity Problems in Directed Graphs In this section, we study the complexity of cycle length modularity problems in directed graphs.  ... 
arXiv:cs/0306131v1 fatcat:j3ajfnk5e5h4rn2euvzdvvflki

Complexity of Cycle Length Modularity Problems in Graphs [chapter]

Edith Hemaspaandra, Holger Spakowski, Mayur Thakur
2004 Lecture Notes in Computer Science  
In this paper, we study the computational complexity of cycle length modularity problems.  ...  Roughly speaking, in a cycle length modularity problem, given an input (undirected or directed) graph, one has to determine whether the graph has a cycle of a specific length (or one of several different  ...  Cycle Length Modularity Problems in Directed Graphs In this section, we study the complexity of cycle length modularity problems in directed graphs.  ... 
doi:10.1007/978-3-540-24698-5_54 fatcat:bpglqfawy5cjnjs4hynwijgxuq

Page 6672 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
In this correspondence, we further study these graphs by first proving the existence of Hamiltonian cycles in any arrangement graph.  ...  (BHR-BAHR-C; Isa Town); Tripathi, Anand (1-MN-C; Minneapolis, MN) Embedding of cycles in arrangement graphs.  ... 

A Characterization of Minimizable Metrics in the Multifacility Location Problem

Hans-Jürgen Bandelt, Victor Chepoi, Alexander V. Karzanov
2000 European journal of combinatorics (Print)  
In [9] , Karzanov showed that the path metric of a graph H is minimizable if and only if all isometric cycles of H have length four and the edges of H can be oriented so that non-adjacent edges in each  ...  4-cycle have opposite orientations along the cycle (such graphs are called frames in [9]).  ...  ACKNOWLEDGEMENT Part of this work was done while the authors were visiting the SFB 343, Universität Bielefeld in fall 1997. A. V. Karzanov was supported in part by RFBR grant 97-01-00115.  ... 
doi:10.1006/eujc.1999.0378 fatcat:7xxipeos4rfhjegzzke2j7a5xa

Weakly modular graphs and nonpositive curvature [article]

Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda
2017 arXiv   pre-print
We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme complexes of modular lattices; we answer Chastand's  ...  We give a local-to-global characterization of weakly modular graphs and their subclasses in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions  ...  Acknowledgements We are very grateful to the anonymous referee for the careful reading of all parts of the paper, for all his efforts and time spent, and for his numerous corrections and improvements.  ... 
arXiv:1409.3892v4 fatcat:abxrludiu5bdlearoqgpigjmcq

Genomics, Pattern Avoidance, and Statistical Mechanics (Dagstuhl Seminar 18451)

Michael Albert, David Bevan, Miklós Bóna, István Miklós, Michael Wagner
2019 Dagstuhl Reports  
We summarize key features of the workshop, such as the three main research areas in which the participants are active, the number and types of talks, and the geographic diversity of the attendees.  ...  We also provide a sampling of the collaborations started at the workshop, and explain why we believe that the workshop was successful, and why we believe it should take place again in the future.  ...  In one version of this problem, Miller had shown in 2009 that there is a permutation of length (n 2 + n)/2 which contains all permutations of length n as subsequences.  ... 
doi:10.4230/dagrep.8.11.1 dblp:journals/dagstuhl-reports/AlbertBBM18 fatcat:j6akx4yqlbgrdfp73uwqzgwale

2213 The origins of modularity in complex machines

Victor Parque, Masakazu Kobayashi, Masatake Higashi
2013 The Proceedings of Design & Systems Conference  
The origins of modularity in complex machines Victor Parque'i, Masakazu Kobayashi'i, Masatake Higashi'i 'i lbyota Technological Institute 2-12-I Hisakateg Tbmpaku-ku, Nagoya 468-85 1 1 , Japan Modularity  ...  We assert thai modularity can emerge fi'om searching desirable machine structures constrained to life cycle costs in manufacturing, maintenance, and disassemblability.  ...  and dissasemblability are important in the life cycle ofthe machine P Reusability depends on the ewerage life cxpcctancy and the complexity of a module.  ... 
doi:10.1299/jsmedsd.2013.23._2213-1_ fatcat:6lur5airobayzfuxabhbf7qzqy

Selecting Sequences of Items via Submodular Maximization

Sebastian Tschiatschek, Adish Singla, Andreas Krause
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Classical algorithms fail to achieve any constant factor approximation guarantees on the problem of selecting sequences of bounded length with maximum utility.  ...  Motivated by many real world applications such as recommendations in online shopping or entertainment, we consider the problem of selecting sequences of items.  ...  In particular, h(•) is a modular function and the graph G contains only self-cycles for all items.  ... 
doi:10.1609/aaai.v31i1.10923 fatcat:o65roim2ejcanfm7nxmoiwwtqm

Drawing graphs using modular decomposition

Charis Papadopoulos, Costas Voglis
2007 Journal of Graph Algorithms and Applications  
In this paper we present an algorithm for drawing an undirected graph G that takes advantage of the structure of the modular decomposition tree of G.  ...  Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges in a bottom-up fashion until it reaches the root of the tree, while at the  ...  Acknowledgements The authors would like to express their thanks to the anonymous referees whose suggestions helped improve the presentation of the paper.  ... 
doi:10.7155/jgaa.00155 fatcat:dxobmywkdzbv7eqtpcszpxyz5u

Drawing Graphs Using Modular Decomposition [chapter]

Charis Papadopoulos, Constantinos Voglis
2006 Lecture Notes in Computer Science  
In this paper we present an algorithm for drawing an undirected graph G that takes advantage of the structure of the modular decomposition tree of G.  ...  Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges in a bottom-up fashion until it reaches the root of the tree, while at the  ...  Acknowledgements The authors would like to express their thanks to the anonymous referees whose suggestions helped improve the presentation of the paper.  ... 
doi:10.1007/11618058_31 fatcat:jtektwfdn5dl5evytclh7zgw6i

Speeding up Networks Mining via Neighborhood Diversity

Gennaro Cordasco, Luisa Gargano, Adele A. Rescigno, Ryuhei Uehara, Giuseppe Prencipe, Martin Farach-Colton
2020 Fun with Algorithms  
However, the proposed novel algorithms allow to improve the computational complexity from a time O(f(mw)⋅ n +m) - where n and m denote, respectively, the number of vertices and edges in the input graph  ...  Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter.  ...  cycle of length 4 in G.  ... 
doi:10.4230/lipics.fun.2021.21 dblp:conf/fun/CordascoGR21 fatcat:anksnea2hjezplia4w7ekqjocm

Minimum 0-Extension Problems on Directed Metrics

Hiroshi Hirai, Ryuhei Mizutani, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We extend the NP-hardness condition of 0-Ext[μ] to 0→-Ext[μ]: If μ cannot be represented as the shortest path metric of an orientable modular graph with an orbit-invariant "directed" edge-length, then  ...  We also show a partial converse: If μ is a directed metric of a modular lattice with an orbit-invariant directed edge-length, then 0→-Ext[μ] is tractable.  ...  It is known [1] that a canonical example of a modular metric is the graph metric of the covering graph of a modular lattice with respect to an orbit-invariant edge-length.  ... 
doi:10.4230/lipics.mfcs.2020.46 dblp:conf/mfcs/0001M20 fatcat:el5rs22mz5emnc2bxpynjhbsry

Page 2458 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
(H) of a graph H has all length-k paths of H as vertices; two such vertices are adjacent in the new graph if their union forms a path or cycle of length & + 1 in H, and if the edge-intersection of both  ...  Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive.  ... 

Mean-Payoff Pushdown Games [article]

Krishnendu Chatterjee, Yaron Velner
2016 arXiv   pre-print
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems.  ...  In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion.  ...  Modular winning strategy problem in NP In this section we will show that the modular winning strategy problem is in NP. Informal description of the solution.  ... 
arXiv:1201.2829v3 fatcat:46sufj6durealjvbx3wvip5ngy

The "log rank" conjecture for modular communication complexity [chapter]

Christoph Meinel, Stephan Waack
1996 Lecture Notes in Computer Science  
In the following, we answer this question in the context of modular communication complexity.  ...  Thus, we are able to determine precisely the modular communication complexity of several problems, such as, e.g., set disjointness, comparability, and undirected graph connectivity.  ...  forms a Hamiltonian cycle, the nondeterministic communication complexity of the problem is (n log log n).  ... 
doi:10.1007/3-540-60922-9_50 fatcat:gpsrsyna3jhszkixhjwuoe2e5a
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