3 Search Results for "Guspiel, Grzegorz"


Document
Sparse Graphs of Twin-Width 2 Have Bounded Tree-Width

Authors: Benjamin Bergougnoux, Jakub Gajarský, Grzegorz Guśpiel, Petr Hliněný, Filip Pokrývka, and Marek Sokołowski

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. Having such a sequence at hand allows to solve many otherwise hard problems efficiently. Our paper focuses on a comparison of twin-width to the more traditional tree-width on sparse graphs. Namely, we prove that if a graph G of twin-width at most 2 contains no K_{t,t} subgraph for some integer t, then the tree-width of G is bounded by a polynomial function of t. As a consequence, for any sparse graph class C we obtain a polynomial time algorithm which for any input graph G ∈ C either outputs a contraction sequence of width at most c (where c depends only on C), or correctly outputs that G has twin-width more than 2. On the other hand, we present an easy example of a graph class of twin-width 3 with unbounded tree-width, showing that our result cannot be extended to higher values of twin-width.

Cite as

Benjamin Bergougnoux, Jakub Gajarský, Grzegorz Guśpiel, Petr Hliněný, Filip Pokrývka, and Marek Sokołowski. Sparse Graphs of Twin-Width 2 Have Bounded Tree-Width. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bergougnoux_et_al:LIPIcs.ISAAC.2023.11,
  author =	{Bergougnoux, Benjamin and Gajarsk\'{y}, Jakub and Gu\'{s}piel, Grzegorz and Hlin\v{e}n\'{y}, Petr and Pokr\'{y}vka, Filip and Soko{\l}owski, Marek},
  title =	{{Sparse Graphs of Twin-Width 2 Have Bounded Tree-Width}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.11},
  URN =		{urn:nbn:de:0030-drops-193130},
  doi =		{10.4230/LIPIcs.ISAAC.2023.11},
  annote =	{Keywords: twin-width, tree-width, excluded grid, sparsity}
}
Document
A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem

Authors: Lech Duraj

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an ?(n²)-time algorithm and a SETH-based conditional lower bound of ?(n^{2-ε}). For LCS, there is also the Masek-Paterson ?(n²/log n)-time algorithm, which does not seem to adapt to LCIS in any obvious way. Hence, a natural question arises: does any (slightly) sub-quadratic algorithm exist for the Longest Common Increasing Subsequence problem? We answer this question positively, presenting a ?(n²/log^a n)-time algorithm for a = 1/6-o(1). The algorithm is not based on memorizing small chunks of data (often used for logarithmic speedups, including the "Four Russians Trick" in LCS), but rather utilizes a new technique, bounding the number of significant symbol matches between the two sequences.

Cite as

Lech Duraj. A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 41:1-41:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{duraj:LIPIcs.STACS.2020.41,
  author =	{Duraj, Lech},
  title =	{{A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{41:1--41:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.41},
  URN =		{urn:nbn:de:0030-drops-119020},
  doi =		{10.4230/LIPIcs.STACS.2020.41},
  annote =	{Keywords: longest common increasing subsequence, log-shaving, matching pairs}
}
Document
Connecting the Dots (with Minimum Crossings)

Authors: Akanksha Agrawal, Grzegorz Guśpiel, Jayakrishnan Madathil, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)


Abstract
We study a prototype Crossing Minimization problem, defined as follows. Let F be an infinite family of (possibly vertex-labeled) graphs. Then, given a set P of (possibly labeled) n points in the Euclidean plane, a collection L subseteq Lines(P)={l: l is a line segment with both endpoints in P}, and a non-negative integer k, decide if there is a subcollection L'subseteq L such that the graph G=(P,L') is isomorphic to a graph in F and L' has at most k crossings. By G=(P,L'), we refer to the graph on vertex set P, where two vertices are adjacent if and only if there is a line segment that connects them in L'. Intuitively, in Crossing Minimization, we have a set of locations of interest, and we want to build/draw/exhibit connections between them (where L indicates where it is feasible to have these connections) so that we obtain a structure in F. Natural choices for F are the collections of perfect matchings, Hamiltonian paths, and graphs that contain an (s,t)-path (a path whose endpoints are labeled). While the objective of seeking a solution with few crossings is of interest from a theoretical point of view, it is also well motivated by a wide range of practical considerations. For example, links/roads (such as highways) may be cheaper to build and faster to traverse, and signals/moving objects would collide/interrupt each other less often. Further, graphs with fewer crossings are preferred for graphic user interfaces. As a starting point for a systematic study, we consider a special case of Crossing Minimization. Already for this case, we obtain NP-hardness and W[1]-hardness results, and ETH-based lower bounds. Specifically, suppose that the input also contains a collection D of d non-crossing line segments such that each point in P belongs to exactly one line in D, and L does not contain line segments between points on the same line in D. Clearly, Crossing Minimization is the case where d=n - then, P is in general position. The case of d=2 is of interest not only because it is the most restricted non-trivial case, but also since it corresponds to a class of graphs that has been well studied - specifically, it is Crossing Minimization where G=(P,L) is a (bipartite) graph with a so called two-layer drawing. For d=2, we consider three basic choices of F. For perfect matchings, we show (i) NP-hardness with an ETH-based lower bound, (ii) solvability in subexponential parameterized time, and (iii) existence of an O(k^2)-vertex kernel. Second, for Hamiltonian paths, we show (i) solvability in subexponential parameterized time, and (ii) existence of an O(k^2)-vertex kernel. Lastly, for graphs that contain an (s,t)-path, we show (i) NP-hardness and W[1]-hardness, and (ii) membership in XP.

Cite as

Akanksha Agrawal, Grzegorz Guśpiel, Jayakrishnan Madathil, Saket Saurabh, and Meirav Zehavi. Connecting the Dots (with Minimum Crossings). In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{agrawal_et_al:LIPIcs.SoCG.2019.7,
  author =	{Agrawal, Akanksha and Gu\'{s}piel, Grzegorz and Madathil, Jayakrishnan and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Connecting the Dots (with Minimum Crossings)}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.7},
  URN =		{urn:nbn:de:0030-drops-104117},
  doi =		{10.4230/LIPIcs.SoCG.2019.7},
  annote =	{Keywords: crossing minimization, parameterized complexity, FPT algorithm, polynomial kernel, W\lbrack1\rbrack-hardness}
}
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