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On r-Simple k-Path and Related Problems Parameterized by k/r
[article]

2020
*
arXiv
*
pre-print

We resolve the wider question

arXiv:1806.09108v2
fatcat:hcu4slsv7rbcra5yt53qunx32a
*by*(a) obtaining a 2^O((*k*/*r*)^2log(*k*/*r*)) (n+log*k*)^O(1)-time algorithm for*r*-*Simple**k*-*Path**on*digraphs*and*a 2^O(*k*/*r*) (n+log*k*)^O(1)-time algorithm for*r*-*Simple**k*-*Path**on*undirected ... In the*r*-*Simple**k*-*Path**problem*, given a digraph G*on*n vertices*and*integers*r*,*k*, decide whether G has an*r*-*simple**k*-*path*, which is a walk where every vertex occurs at most*r*times*and*the total number ... Directed*r*-*Simple**k*-*Path*: FPT In this section, we focus*on*the proof of the following theorem. Theorem 4. Directed*r*-*Simple**k*-*Path*is FPT*parameterized**by**k*/*r*. ...##
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Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs

2005
*
ACM Transactions on Algorithms
*

In this article we prove that the (

doi:10.1145/1077464.1077468
fatcat:hfeciu7igncabltwzyokqs2fkm
*k*,*r*)-center*problem*,*parameterized**by**k**and**r*, is fixed-parameter tractable (FPT)*on*planar graphs, i.e., it admits an algorithm of complexity f (*k*,*r*)n O(1) where the ... The (*k*,*r*)-center*problem*asks whether an input graph G has ≤*k*vertices (called centers) such that every vertex of G is within distance ≤*r*from some center. ...*One*can easily observe that for any*r*the*problem*of checking whether an input graph has a (*k*,*r*)-center,*parameterized**by**k*is W [2]-hard*by*a reduction from dominating set. ...##
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Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs
[chapter]

2003
*
Lecture Notes in Computer Science
*

In this article we prove that the (

doi:10.1007/3-540-45061-0_65
fatcat:k3gzdcsewrf4zmgg4mfro2fp2u
*k*,*r*)-center*problem*,*parameterized**by**k**and**r*, is fixed-parameter tractable (FPT)*on*planar graphs, i.e., it admits an algorithm of complexity f (*k*,*r*)n O(1) where the ... The (*k*,*r*)-center*problem*asks whether an input graph G has ≤*k*vertices (called centers) such that every vertex of G is within distance ≤*r*from some center. ...*One*can easily observe that for any*r*the*problem*of checking whether an input graph has a (*k*,*r*)-center,*parameterized**by**k*is W [2]-hard*by*a reduction from dominating set. ...##
###
R&D Investments with Competitive Interactions

2004
*
Review of Finance
*

These benefits to society are countered

doi:10.1007/s10679-004-2543-z
fatcat:dslcmwxmnvhhvbzmktdtkdmjrm
*by*increased total investment costs in*R*&D*and*lower aggregate value of the*R*&D investment projects. ... Implementation of the model shows that competition in*R*&D not only increases production*and*reduces prices, but also shortens the time of developing the product*and*increases the probability of a successful ... This is done*by*first simulating 100,000 discretizised 23 sample*paths*of the three governing state variables Y ,*K*1 ,*and**K*2 . ...##
###
A Bayesian Analysis of Nuclear Deformation Properties with Skyrme Energy Functionals
[article]

2020
*
arXiv
*
pre-print

In spite of numerous scientific

arXiv:2006.02906v1
fatcat:fdnyyinnhbff5g2rrwwlpsmf5m
*and*practical applications, there is still no comprehensive theoretical description of the nuclear fission process based solely*on*protons, neutrons*and*their interactions ... In spite of being fully quantum-mechanical*and*rooted in the theory of nuclear forces, DFT still depends*on*a dozen or so parameters characterizing the energy functional. ... Department of Energy*by*Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344*and*was supported*by*the LLNL-LDRD Program under Project No. 18-ERD-008. ...##
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FAIDECS: Fair Decentralized Event Correlation
[chapter]

2011
*
Lecture Notes in Computer Science
*

In contrast to traditional settings, deliver is

doi:10.1007/978-3-642-25821-3_12
fatcat:siobqi7tk5cyrc2wn6twpel2xa
*parameterized**by*a "subscription" Φ*and*delivers ordered sets of typed messages representing events. ... ∪ { e, ts } ∪ R17:for all e , t ∈*R*ordered*on*t | t < min T (S[T ]) do18:for all Φ l in order do19:if enqueue(e , Φ l , Q l ) then 20:*R*←*R*\{ e , t }21:[e1, ..., e*k*] ← match(∅, Φ l , Q l ) e1, ..., ...##
###
Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
[article]

2015
*
arXiv
*
pre-print

Our technique works for a large class of circuits,

arXiv:1411.6756v5
fatcat:pt54utshmfayvnj2ebrgbvzqdi
*and*in particular it can be used to derandomize the result of Abasi et al. for*r*-*Simple**k*-*Path*. ... Most often, the complexity of the*problem*increases with the relaxation variable, but very recently Abasi et al. have given a surprising example of a*problem*---*r*-*Simple**k*-*Path*--- that can be solved ... We have considered the*r*-*Simple**k*-*Path**problem*where the weights are*on*the vertices. ...##
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Parameterized Algorithms and Data Reduction for Safe Convoy Routing

2018
*
Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
*

E), two vertices s, t ∈ V ,

doi:10.4230/oasics.atmos.2018.10
dblp:conf/atmos/BevernFT18
fatcat:zyneram6v5h6jkujxn277vufhy
*and*two integers*k*, , we search for a*simple*s-tpath with at most*k*vertices*and*at most neighbors. ... We study the*problem*in two types of transportation networks: graphs with small crossing number, as formed*by*road networks,*and*tree-like graphs, as formed*by*waterways. ...*By*Lemma 2.21, Construction 2.19 is a polynomial parameter transformation from Multicolored Clique*parameterized**by**k*log n to SSP*parameterized**by*vc +*r*in*K**r*,*r*-free graphs. ...##
###
Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
[chapter]

2015
*
Lecture Notes in Computer Science
*

For example, the

doi:10.1007/978-3-662-48350-3_46
fatcat:m25u27cdvbgw7ch47xsydankaa
*k*-*Path**problem*is generalized to*r*-*Simple**k*-*Path*where the task is to find a walk of length*k*that never visits any vertex more than*r*times. ... In this paper we consider generalized versions of four wellstudied*problems*in*parameterized*complexity*and*exact exponential time algorithms:*k*-*Path*, Set Packing, Multilinear Monomial Testing*and*Hamiltonian ... We have considered the*r*-*Simple**k*-*Path**problem*where the weights are*on*the vertices. ...##
###
An Elastic Energy Minimization Framework for Mean Contour Calculation
[article]

2019
*
arXiv
*
pre-print

With respect to this representation the re-

arXiv:1901.02823v1
fatcat:n3edso2tdfh7rdnjyo52kte6ka
*parameterization*group acts*by*isometries*and*the distance has well defined meaning: the sum of the central second moments of the coordinate functions. ... The chosen representation space - the position vector rescaled*by*square root velocity - is a real valued vector space*on*which the imposed L2 metric is used to define the distance function. ...*On*the other hand, the predetermined sampling strategy of the landmark points is*related*to the fixed*parameterization*of the contours. ...##
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Grid Recognition: Classical and Parameterized Computational Perspectives
[article]

2021
*
arXiv
*
pre-print

We show that the

arXiv:2106.16180v1
fatcat:myw6oc72jvbmpoxc5dwqysvewa
*problem*is para-NP-hard*parameterized**by*a_G, but FPT*parameterized**by*a_G*on*trees, as well as FPT*parameterized**by**k*+a_G. ... Grid graphs,*and*, more generally,*k*×*r*grid graphs, form*one*of the most basic classes of geometric graphs. ... Grid Embedding (*and*hence also*k*×*r*-Grid Embedding) is para-NP- hard*parameterized**by*aG . When we enrich the*parameterization**by**k*, then*k*×*r*-Grid Embedding*problem*becomes FPT. ...##
###
Stability of the in-phase travelling wave solutions in a pair of coupled nerve fibers

1995
*
Indiana University Mathematics Journal
*

Conditions are given which guarantee the existence

doi:10.1512/iumj.1995.44.1984
fatcat:jl2fdy3srbcabkvr7xqy42stmm
*and*stability of the wave. ... Two advances in the geometric techniques in the stability analysis of travelling waves are given: the first involves the Maslov Index,*and*the other the Exchange Lemma. ... The*relation*between C(2)*and**R*is given*by*the horizontal distance traveled in C(2) projected onto*R*, the covering space of S 1 . ...##
###
On Problems without Polynomial Kernels (Extended Abstract)
[chapter]

2008
*
Lecture Notes in Computer Science
*

These

doi:10.1007/978-3-540-70575-8_46
fatcat:sd3fuidkzvay7hvljo257xpvjy
*problems*include*k*-*Path*,*k*-Cycle,*k*-Exact Cycle,*k*-Short Cheap Tour,*k*-Graph Minor Order Test,*k*-Cutwidth,*k*-Search Number,*k*-Pathwidth,*k*-Treewidth,*k*-Branchwidth,*and*several optimization*problems*...*parameterized**by*treewidth or cliquewidth. ... The fourth author would also like to thank Moritz Müller for reviewing several preliminary versions,*and*especially for the countless (*and*sometimes endless) debates*on**related*topics. ...##
###
Parameterized Complexity of Independent Set in H-Free Graphs

2019
*
International Symposium on Parameterized and Exact Computation
*

Finally, we present positive

doi:10.4230/lipics.ipec.2018.17
dblp:conf/iwpec/BonnetBCTW18
fatcat:bpbn35perzbhpcsbg4tgk7y4vu
*and*negative results*on*the existence of polynomial (Turing) kernels for several graphs H. ... Given that the*problem*remains N P -hard for most graphs H, we study its fixed-parameter tractability*and*make progress towards a dichotomy between F P T*and*W [1]-hard cases. ... A very*simple*case concerns*K**r*-free graphs, that is, graphs excluding a clique of size*r*. ...##
###
Extended static checking
[chapter]

1998
*
Programming Concepts and Methods PROCOMET '98
*

an acknowledgment of the authors

doi:10.1007/978-0-387-35358-6_1
fatcat:mktrvpe7rjgopdq6e6rfkane64
*and*individual contributors to the work;*and*all applicable portions of the copyright notice. ... The checker uses an automatic theorem-prover to reason about the semantics of conditional statements, loops, procedure*and*method calls,*and*exceptions. The checker has been implemented for Modula-3. ... Shun-Tak Leung*and*Allan Heydon provided comments*on*drafts of this paper. The whole project benefited from helpful suggestions from Jim Horning*and*Raymie Stata. ...
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