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

Gregory Gutin, Magnus Wahlström, Meirav Zehavi
2020 arXiv   pre-print
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  ...  We resolve the wider question 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  ...  Reduction to a Simpler Problem In order to prove Theorem 4, we begin with two simple claims that reduce the Directed r-Simple k-Path problem to a special case of a related problem that is defined as follows  ...

### Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs

Erik D. Demaine, Fedor V. Fomin, Mohammadtaghi Hajiaghayi, Dimitrios M. Thilikos
2005 ACM Transactions on Algorithms
In this article we prove that the (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 -hard by a reduction from dominating set.  ...

### Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs [chapter]

Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Hajiaghayi, Dimitrios M. Thilikos
2003 Lecture Notes in Computer Science
In this article we prove that the (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 -hard by a reduction from dominating set.  ...

### R&D Investments with Competitive Interactions

K. R. Miltersen, E. S. Schwart
2004 Review of Finance
These benefits to society are countered 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]

N. Schunck, K. R. Quinlan, J. Bernstein
2020 arXiv   pre-print
In spite of numerous scientific 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.  ...

### FAIDECS: Fair Decentralized Event Correlation [chapter]

Gregory Aaron Wilkin, K. R. Jayaram, Patrick Eugster, Ankur Khetrapal
2011 Lecture Notes in Computer Science
In contrast to traditional settings, deliver is parameterized by a "subscription" Φ and delivers ordered sets of typed messages representing events.  ...  Forwarding of events received by mergers from their respective parent mergers (lef t) or processes for merged event types (right) happens without interruptions by other events and can be achieved by simple  ...

### Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints [article]

Ariel Gabizon, Daniel Lokshtanov, Michal Pilipczuk
2015 arXiv   pre-print
Our technique works for a large class of circuits, 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  ...  In particular, they study the r-Simple k-Path problem.  ...

### Parameterized Algorithms and Data Reduction for Safe Convoy Routing

René Van Bevern, Till Fluschnik, Oxana Yu. Tsidulko, Michael Wagner
2018 Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
E), two vertices s, t ∈ V , 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]

Ariel Gabizon, Daniel Lokshtanov, Michał Pilipczuk
2015 Lecture Notes in Computer Science
For example, the 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  ...  In particular, they study the r-Simple k-Path problem.  ...

### An Elastic Energy Minimization Framework for Mean Contour Calculation [article]

Jozsef Molnar, Michael Barbier, Winnok H. De Vos, Peter Horvath
2019 arXiv   pre-print
With respect to this representation the re-parameterization group acts by isometries and the distance has well defined meaning: the sum of the central second moments of the coordinate functions.  ...  In this paper we propose a contour mean calculation and interpolation method designed for averaging manual delineations of objects performed by experts and interpolate 3D layer stack images.  ...  Problem (10) can be interpreted as simple extreme value problem wrt the centroid coordinates R 0 and such the condition: d n i=1¸( R 0 − R i (t)) 2 i dt dR 0 . = 0 (11) provides the following solution  ...

### The parameterization of wave-particle interactions in the Outer Radiation Belt

Clare E. J. Watt, I. J. Rae, K. R. Murphy, C. Anekallu, S. N. Bentley, C. Forsyth
2017 Journal of Geophysical Research - Space Physics
We suggest that other techniques such as stochastic parameterization will lead to a better characterization of subgrid diffusion physics in the Outer Radiation Belt.  ...  We show that magnetospheric wave power is not normally distributed in time and that geomagnetic activity does not provide a deterministic proxy for the temporal variability of wave activity.  ...  The region spans radial distances of 2.5 < r < 7 R E , where R E is an Earth radius, although the size and location of the Outer Radiation Belt varies dramatically in response to solar wind variability  ...

### Grid Recognition: Classical and Parameterized Computational Perspectives [article]

Siddharth Gupta, Guy Sa'ar, Meirav Zehavi
2021 arXiv   pre-print
We show that the 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.  ...

### On Problems without Polynomial Kernels (Extended Abstract) [chapter]

Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, Danny Hermelin
2008 Lecture Notes in Computer Science
These 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.  ...

### Stability of the in-phase travelling wave solutions in a pair of coupled nerve fibers

Amitabha Bose, Christopher K. R. T. Jones
1995 Indiana University Mathematics Journal
Conditions are given which guarantee the existence 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 .  ...

### Parameterized Complexity of Independent Set in H-Free Graphs

Édouard Bonnet, Nicolas Bousquet, Pierre Charbit, Stéphan Thomassé, Rémi Watrigant, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation
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 -hard cases.  ...  We first show that MIS remains W -hard in graphs forbidding simultaneously K 1,4 , any finite set of cycles of length at least 4, and any finite set of trees with at least two branching vertices.  ...  A very simple case concerns K r -free graphs, that is, graphs excluding a clique of size r.  ...
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