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Complexity of Cycle Length Modularity Problems in Graphs
[article]

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*. ...

##
###
Complexity of Cycle Length Modularity Problems in Graphs
[chapter]

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*. ...

##
###
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

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. ...

##
###
Weakly modular graphs and nonpositive curvature
[article]

2017
*
arXiv
*
pre-print

We resolve some open

arXiv:1409.3892v4
fatcat:abxrludiu5bdlearoqgpigjmcq
*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. ...##
###
Genomics, Pattern Avoidance, and Statistical Mechanics (Dagstuhl Seminar 18451)

2019
*
Dagstuhl Reports
*

We summarize key features

doi:10.4230/dagrep.8.11.1
dblp:journals/dagstuhl-reports/AlbertBBM18
fatcat:j6akx4yqlbgrdfp73uwqzgwale
*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. ...##
###
2213 The origins of modularity in complex machines

2013
*
The Proceedings of Design & Systems Conference
*

The origins

doi:10.1299/jsmedsd.2013.23._2213-1_
fatcat:6lur5airobayzfuxabhbf7qzqy
*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. ...##
###
Selecting Sequences of Items via Submodular Maximization

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

doi:10.1609/aaai.v31i1.10923
fatcat:o65roim2ejcanfm7nxmoiwwtqm
*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. ...##
###
Drawing graphs using modular decomposition

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. ...

##
###
Drawing Graphs Using Modular Decomposition
[chapter]

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. ...

##
###
Speeding up Networks Mining via Neighborhood Diversity

2020
*
Fun with Algorithms
*

However, the proposed novel algorithms allow to improve the computational

doi:10.4230/lipics.fun.2021.21
dblp:conf/fun/CordascoGR21
fatcat:anksnea2hjezplia4w7ekqjocm
*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. ...##
###
Minimum 0-Extension Problems on Directed Metrics

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We extend the NP-hardness condition

doi:10.4230/lipics.mfcs.2020.46
dblp:conf/mfcs/0001M20
fatcat:el5rs22mz5emnc2bxpynjhbsry
*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*. ...##
###
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]

2016
*
arXiv
*
pre-print

Two-player games on

arXiv:1201.2829v3
fatcat:46sufj6durealjvbx3wvip5ngy
*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. ...##
###
The "log rank" conjecture for modular communication complexity
[chapter]

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). ...

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