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Finding Detours is Fixed-parameter Tractable
[article]

2016
*
arXiv
*
pre-print

Using insights into structural graph theory, we prove that Longest

arXiv:1607.07737v1
fatcat:xg3fkjj6nfff3c4p464uh2sk74
*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*. ...##
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Finding Detours is Fixed-Parameter Tractable * †

unpublished

Using insights into structural graph theory, we prove that Longest

fatcat:spljtohjuneq5ez6umzqczpipy
*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*. ...##
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Spanners of bounded degree graphs

2011
*
Information Processing Letters
*

In particular, this implies that

doi:10.1016/j.ipl.2010.10.021
fatcat:gw6jr2js4fchzbi62lscizrhj4
*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 ...##
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Reconfiguring Undirected Paths
[article]

2019
*
arXiv
*
pre-print

We show that this problem may be solved in linear time in trees, and

arXiv:1905.00518v1
fatcat:4tkir6dnazbnhjswoz37wwmgce
*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. ...##
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Crossing-Optimal Extension of Simple Drawings
[article]

2020
*
arXiv
*
pre-print

In particular, we show that the problem of inserting edges into a simple drawing

arXiv:2012.07457v1
fatcat:w3z42n44yrbnrdjxaanvna7kp4
*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. ...##
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On Minimizing Crossings in Storyline Visualizations
[chapter]

2015
*
Lecture Notes in Computer Science
*

Lastly, we show that, in the general case, minimizing the number of crossings in a storyline visualization

doi:10.1007/978-3-319-27261-0_16
fatcat:i5sqvivjwffrhj2kup4ibif2y4
*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. ...##
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Wireless scheduling

2009
*
2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
*

space
•

doi:10.1109/wiopt.2009.5291566
dblp:conf/wiopt/Chiang09
fatcat:5ybawrdpy5h7vn6ot6y6rqlmkm
*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? ...##
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On Finding Optimal Polytrees

2012
*
arXiv
*
pre-print

We contrast this positive result by showing that if we

arXiv:1208.1692v2
fatcat:gnnwcwmjv5hyrguc2rfbf25gty
*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*? ...##
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On finding optimal polytrees

2015
*
Theoretical Computer Science
*

We contrast this positive result by showing that if we

doi:10.1016/j.tcs.2015.05.012
fatcat:jvqvrzuj6bazjp4pn6zu27cku4
*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*? ...##
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Model Checking for Successor-Invariant First-Order Logic on Minor-Closed Graph Classes

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

doi:10.1109/lics.2013.19
dblp:conf/lics/EickmeyerKK13
fatcat:yv6s47yuxjel3fc32dd2au7ym4
*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*. ...##
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Fixed-Parameter Sensitivity Oracles
[article]

2021
*
arXiv
*
pre-print

We combine ideas from distance sensitivity oracles (DSOs) and

arXiv:2112.03059v1
fatcat:ooac3rw4szh63icloztu7jdymm
*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. ...##
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Pursuing a fast robber on a graph

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

doi:10.1016/j.tcs.2009.12.010
fatcat:nzbkea3bqbd6nl66mcoqtiwnoa
*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*? ...##
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Model-checking for successor-invariant first-order formulas on graph classes of bounded expansion

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

doi:10.1109/lics.2017.8005115
dblp:conf/lics/HeuvelKPQRS17
fatcat:jdqaqsza6rgi3ke7ldtaekaj6i
*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*. ...##
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Model-Checking for Successor-Invariant First-Order Formulas on Graph Classes of Bounded Expansion
[article]

2017
*
arXiv
*
pre-print

In this work we show that the model-checking problem for successor-invariant formulas

arXiv:1701.08516v2
fatcat:pmoy3mbenjchxa6xr6sbapy72y
*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*. ...##
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Optimal route decision with a geometric ground-airborne hybrid model under weather uncertainty

2011
*
Procedia - Social and Behavioral Sciences
*

Based on the numerical analysis, we

doi:10.1016/j.sbspro.2011.04.531
fatcat:fnltzghsk5f5bmbh2pwltjd5ty
*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 ...
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