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Finding Detours is Fixed-parameter Tractable [article]

Ivona Bezáková, Radu Curticapean, Holger Dell, Fedor V. Fomin
2016 arXiv   pre-print
Using insights into structural graph theory, we prove that Longest Detour is fixed-parameter tractable (FPT) on undirected graphs and actually even admits a single-exponential algorithm, that is, one of  ...  We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for  ...  Exact Detour is fixed-parameter tractable.  ... 
arXiv:1607.07737v1 fatcat:xg3fkjj6nfff3c4p464uh2sk74

Finding Detours is Fixed-Parameter Tractable * †

Ivona Bezáková, Radu Curticapean, Holger Dell, Fedor Fomin
unpublished
Using insights into structural graph theory, we prove that Longest Detour is fixed-parameter tractable (FPT) on undirected graphs and actually even admits a single-exponential algorithm, that is, one of  ...  We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for  ...  Exact Detour is fixed-parameter tractable.  ... 
fatcat:spljtohjuneq5ez6umzqczpipy

Spanners of bounded degree graphs

Fedor V. Fomin, Petr A. Golovach, Erik Jan van Leeuwen
2011 Information Processing Letters  
In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree.  ...  We prove that for fixed k, w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree.  ...  They proved that the problem of finding a k-spanner of treewidth at most w in a given planar graph G is fixed-parameter tractable parameterized by k and w, and for every fixed k and w, this problem can  ... 
doi:10.1016/j.ipl.2010.10.021 fatcat:gw6jr2js4fchzbi62lscizrhj4

Reconfiguring Undirected Paths [article]

Erik D. Demaine, David Eppstein, Adam Hesterberg, Kshitij Jain, Anna Lubiw, Ryuhei Uehara, Yushi Uno
2019 arXiv   pre-print
We show that this problem may be solved in linear time in trees, and is fixed-parameter tractable when parameterized either by the cyclomatic number of the input graph or by the length of the path.  ...  We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove  ...  Parameterized by path length In this section we show that path reconfiguration is fixed-parameter tractable when parameterized by path length.  ... 
arXiv:1905.00518v1 fatcat:4tkir6dnazbnhjswoz37wwmgce

Crossing-Optimal Extension of Simple Drawings [article]

Robert Ganian, Thekla Hamm, Fabian Klute, Irene Parada, Birgit Vogtenhuber
2020 arXiv   pre-print
In particular, we show that the problem of inserting edges into a simple drawing is fixed-parameter tractable when parameterized by the number of edges to insert and an upper bound on newly created crossings  ...  Moreover, using a different approach, we provide a single-exponential fixed-parameter algorithm for the case in which we are only trying to insert a single edge into the drawing.  ...  Z is fixed-parameter tractable. Proof. We provide a fixed-parameter algorithm for Z.  ... 
arXiv:2012.07457v1 fatcat:w3z42n44yrbnrdjxaanvna7kp4

On Minimizing Crossings in Storyline Visualizations [chapter]

Irina Kostitsyna, Martin Nöllenburg, Valentin Polishchuk, André Schulz, Darren Strash
2015 Lecture Notes in Computer Science  
Lastly, we show that, in the general case, minimizing the number of crossings in a storyline visualization is fixed-parameter tractable, when parameterized on the number of characters $k$.  ...  ^2m)$, where $m$ is the number of meetings.  ...  We show that the storyline problem is fixed-parameter tractable when parameterized on k.  ... 
doi:10.1007/978-3-319-27261-0_16 fatcat:i5sqvivjwffrhj2kup4ibif2y4

Wireless scheduling

Mung Chiang
2009 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks  
space • Parameterize into tradeoff curves • Three 2D projections: e.g., Stability-delay tradeoff for a fixed complexity Yi Proutiere Chiang 2008 3D Tradeoff Throughput Delay Complexity  ...  Computation and Communication x l (t) = Q l (t) max h P k∈L(t(l)) Q k (t), P k∈L(r(l)) Q k (t) i • Detour: Distributed Algorithm in Networking How distributed is distributed?  ... 
doi:10.1109/wiopt.2009.5291566 dblp:conf/wiopt/Chiang09 fatcat:5ybawrdpy5h7vn6ot6y6rqlmkm

On Finding Optimal Polytrees

Serge Gaspers, Mikko Koivisto, Mathieu Liedloff, Sebastian Ordyniak, Stefan Szeider
2012 arXiv   pre-print
We contrast this positive result by showing that if we parameterize by the number of deleted nodes, a somewhat more powerful parameter, the problem is not fixed-parameter tractable, subject to a complexity-theoretic  ...  The order of the polynomial time bound depends on this constant, hence the algorithm does not establish fixed-parameter tractability when parameterized by the number of deleted arcs.  ...  Can we find other restrictions under which the k-branching problem becomes fixed-parameter tractable?  ... 
arXiv:1208.1692v2 fatcat:gnnwcwmjv5hyrguc2rfbf25gty

On finding optimal polytrees

Serge Gaspers, Mikko Koivisto, Mathieu Liedloff, Sebastian Ordyniak, Stefan Szeider
2015 Theoretical Computer Science  
We contrast this positive result by showing that if we parameterize by the number of deleted nodes, a somewhat more powerful parameter, the problem is not fixed-parameter tractable, subject to a complexity-theoretic  ...  The order of the polynomial time bound depends on this constant, hence the algorithm does not establish fixed-parameter tractability when parameterized by the number of deleted arcs.  ...  Can we find other restrictions under which the k-branching problem becomes fixed-parameter tractable?  ... 
doi:10.1016/j.tcs.2015.05.012 fatcat:jvqvrzuj6bazjp4pn6zu27cku4

Model Checking for Successor-Invariant First-Order Logic on Minor-Closed Graph Classes

Kord Eickmeyer, Ken-Ichi Kawarabayashi, Stephan Kreutzer
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
The supergraphs may in general contain H minors, but they still exclude some possible larger minor H , so by results of Flum and Grohe [20] model checking on these graphs is still fixed-parameter tractable  ...  In this paper we significantly improve the latter result and show that successor-invariant first-order logic is tractable on any class of graphs excluding a fixed minor.  ...  Obviously, the concept of fixed-parameter tractability crucially relies on the choice of parameter.  ... 
doi:10.1109/lics.2013.19 dblp:conf/lics/EickmeyerKK13 fatcat:yv6s47yuxjel3fc32dd2au7ym4

Fixed-Parameter Sensitivity Oracles [article]

Davide Bilò, Katrin Casel, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, J.A. Gregor Lagodzinski, Martin Schirneck, Simon Wietheger
2021 arXiv   pre-print
We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems.  ...  We study the problem, given a directed unweighted graph with a fixed source s and parameters f and k, to construct a polynomial-sized oracle that efficiently reports, for any target vertex v and set F  ...  Finding Detours is Fixed-Parameter Tractable. SIAM Journal on Discrete Mathematics, 33:2326–2345, 2019.  ... 
arXiv:2112.03059v1 fatcat:ooac3rw4szh63icloztu7jdymm

Pursuing a fast robber on a graph

Fedor V. Fomin, Petr A. Golovach, Jan Kratochvíl, Nicolas Nisse, Karol Suchan
2010 Theoretical Computer Science  
In this paper we prove that computing the minimum number of cops that are guaranteed to catch a robber on a given graph is NP-hard and that the parameterized version of the problem is W[2]-hard; the proof  ...  We show that on split graphs, the problem is polynomially solvable if s = 1 but is NP-hard if s = 2.  ...  The first is, what is the complexity of the problem when k is part of the input? Another is the problem fixed parameter tractable?  ... 
doi:10.1016/j.tcs.2009.12.010 fatcat:nzbkea3bqbd6nl66mcoqtiwnoa

Model-checking for successor-invariant first-order formulas on graph classes of bounded expansion

Jan van den Heuvel, Stephan Kreutzer, Michal Pilipczuk, Daniel A. Quiroz, Roman Rabinovich, Sebastian Siebertz
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
In this work we show that the model-checking problem for successor-invariant formulas is fixed-parameter tractable on any class of finite structures whose underlying Gaifman graphs form a class of bounded  ...  planar [13] , excludes a fixed minor [11] or a fixed topological minor [10, 25] .  ...  to a class where model-checking first-order logic is fixed-parameter tractable.  ... 
doi:10.1109/lics.2017.8005115 dblp:conf/lics/HeuvelKPQRS17 fatcat:jdqaqsza6rgi3ke7ldtaekaj6i

Model-Checking for Successor-Invariant First-Order Formulas on Graph Classes of Bounded Expansion [article]

Jan van den Heuvel and Stephan Kreutzer and Michał Pilipczuk and Daniel A. Quiroz and Roman Rabinovich and Sebastian Siebertz
2017 arXiv   pre-print
In this work we show that the model-checking problem for successor-invariant formulas is fixed-parameter tractable on any class of finite structures whose underlying Gaifman graphs form a class of bounded  ...  planar [Engelmann et al., 2012], excludes a fixed minor [Eickmeyer et al., 2013] or a fixed topological minor [Eickmeyer and Kawarabayashi, 2016; Kreutzer et al., 2016].  ...  to a class where model-checking first-order logic is fixed-parameter tractable.  ... 
arXiv:1701.08516v2 fatcat:pmoy3mbenjchxa6xr6sbapy72y

Optimal route decision with a geometric ground-airborne hybrid model under weather uncertainty

Yoonjin Yoon, Mark Hansen, Michael O. Ball
2011 Procedia - Social and Behavioral Sciences  
Based on the numerical analysis, we find that ground-holding is effective only when combined with the nominal route.  ...  We propose a solution algorithm that guarantees to find the global optimum of the hybrid-DRM.  ...  Since the cost ratio between the ground and airborne delay is not fixed, we treat the cost ratio as an additional model parameter and find the optimal combination of the ground delay and the route choice  ... 
doi:10.1016/j.sbspro.2011.04.531 fatcat:fnltzghsk5f5bmbh2pwltjd5ty
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