5 Search Results for "Dębski, Michał"

Document
DOI: 10.4230/LIPIcs.WADS.2025.44
Streaming Algorithms for Conflict-Free Coloring

Authors: Rogers Mathew, Fahad Panolan, and Seshikanth

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Conflict-free coloring of a hypergraph ℋ = (V,ℰ) using k colors is a function f:V → {1,2, …, k} such that for all E ∈ ℰ, there exists a vertex v ∈ E with a unique color. That is, f(v)≠ f(u) for all u ∈ E ⧵ {v}. The minimum k for which ℋ has a conflict-free coloring using k colors is called the conflict-free chromatic number of ℋ. For a simple graph G, a conflict-free coloring of the hypergraph with vertex set V(G) and edge set being the set of all closed neighborhoods of the vertices in G is called a conflict-free closed neighborhood (CFCN) coloring of G. CFCN chromatic number, denoted by χ_{CN}(G), is the minimum number of colors used in a conflict-free closed neighborhood coloring of G. Analogously, we define conflict-free open neighborhood (CFON) coloring and CFON chromatic number, χ_{ON}(G), of a graph G. There are various works on proving upper and lower bounds of χ_{ON}(G) and χ_{CN}(G). In this work, we develop streaming algorithms for CFCN and CFON coloring of a graph where the number of colors used matches the best-known upper bounds of χ_{ON}(G) and χi_{CN}(G). Our algorithms use as input an edge stream of the graph G in the insertion-only model. Our results and the best-known bounds for χ_{ON}(G) and χ_{CN}(G) are given below. 1. Pach and Tardos [Combinatorics, Probability and Computing, 2009] showed that, for any n vertex graph G, χ_{CN}(G) = O(ln² n). Glebov, Szabó and Tardos [Combinatorics, Probability and Computing, 2014] showed the existence of graphs G with χ_{CN}(G) = Ω(ln² n). We design a randomized single-pass semi-streaming algorithm (i.e., it uses O(n ln n) space that, given an n-vertex graph G, outputs a CFCN coloring of G using O(ln² n) colors with probability at least (1-2/n). 2. Bhyravarapu, Kalyanasundaram, Mathew [Journal of Graph Theory, 2021] showed that for a graph G with maximum degree Δ, χ_{CN}(G) = O(ln² Δ). The methods used by our algorithms give rise to a simpler, alternate proof for this bound. 3. It is known that χ_{ON}(G) ≤ 1/2 + √{2n + 1/4} (See Pach and Tardos [Combinatorics, Probability and Computing, 2009] and Ph.D. thesis of Cheilaris). This bound is asymptotically tight. - We design a deterministic single-pass O(n√n) space streaming algorithm that, given a graph G on n vertices, finds a CFON coloring using 2√n colors. - We design a randomized, single-pass, semi-streaming algorithm to find a CFON coloring of a graph G using O(√n ln² n) colors with success probability at least (1-2/n). 4. It is known that χ_{ON}(G) ≤ Δ+1, where Δ is the maximum degree of a vertex in G. Further, there are graphs G known with χ_{ON}(G) = Δ + 1. We design a randomized two-pass semi-streaming algorithm (uses O(1/(ε²) n ln³ n) space) that outputs a CFON coloring of G using (1+ε)Δ colors, for any ε > 0, with a probability at least (1-1/n).
Cite as

Rogers Mathew, Fahad Panolan, and Seshikanth. Streaming Algorithms for Conflict-Free Coloring. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mathew_et_al:LIPIcs.WADS.2025.44,
  author =	{Mathew, Rogers and Panolan, Fahad and Seshikanth},
  title =	{{Streaming Algorithms for Conflict-Free Coloring}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.44},
  URN =		{urn:nbn:de:0030-drops-242756},
  doi =		{10.4230/LIPIcs.WADS.2025.44},
  annote =	{Keywords: Streaming algorithm, conflict-free coloring, vertex coloring, randomized algorithms}
}
Artifact
Software
DOI: 10.4230/artifacts.22479
torus packing for multisets

Authors: Élie de Panafieu

Abstract
Cite as

Élie de Panafieu. torus packing for multisets (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22479,
   title = {{torus packing for multisets}}, 
   author = {de Panafieu, \'{E}lie},
   note = {Software, version 1.0., swhId: \href{https://archive.softwareheritage.org/swh:1:dir:2eb591ca09fb8739e2135e17b5f595b7f25ed924;origin=https://gitlab.com/depanafieuelie/torus-packing-for-multisets;visit=swh:1:snp:977c7dfa75b83551f7238790b259989a998825a6;anchor=swh:1:rev:a59cfd49aabd0d6c7eab651836b2ebac621ccf31}{\texttt{swh:1:dir:2eb591ca09fb8739e2135e17b5f595b7f25ed924}} (visited on 2024-11-28)},
   url = {https://gitlab.com/depanafieuelie/torus-packing-for-multisets},
   doi = {10.4230/artifacts.22479},
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.22
Languages Given by Finite Automata over the Unary Alphabet

Authors: Wojciech Czerwiński, Maciej Dębski, Tomasz Gogasz, Gordon Hoi, Sanjay Jain, Michał Skrzypczak, Frank Stephan, and Christopher Tan

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary and n the number of states of the finite automata considered. The following main results are obtained: 1) Equality and inclusion of NFAs can be decided within time 2^O((n log n)^{1/3}); previous upper bound 2^O((n log n)^{1/2}) was by Chrobak (1986) via DFA conversion. 2) The state complexity of operations of UFAs (unambiguous finite automata) increases for complementation and union at most by quasipolynomial; however, for concatenation of two n-state UFAs, the worst case is an UFA of at least 2^Ω(n^{1/6}) states. Previously the upper bounds for complementation and union were exponential-type and this lower bound for concatenation is new.
Cite as

Wojciech Czerwiński, Maciej Dębski, Tomasz Gogasz, Gordon Hoi, Sanjay Jain, Michał Skrzypczak, Frank Stephan, and Christopher Tan. Languages Given by Finite Automata over the Unary Alphabet. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{czerwinski_et_al:LIPIcs.FSTTCS.2023.22,
  author =	{Czerwi\'{n}ski, Wojciech and D\k{e}bski, Maciej and Gogasz, Tomasz and Hoi, Gordon and Jain, Sanjay and Skrzypczak, Micha{\l} and Stephan, Frank and Tan, Christopher},
  title =	{{Languages Given by Finite Automata over the Unary Alphabet}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.22},
  URN =		{urn:nbn:de:0030-drops-193959},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.22},
  annote =	{Keywords: Nondeterministic Finite Automata, Unambiguous Finite Automata, Upper Bounds on Runtime, Conditional Lower Bounds, Languages over the Unary Alphabet}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.14
Computing Homomorphisms in Hereditary Graph Classes: The Peculiar Case of the 5-Wheel and Graphs with No Long Claws

Authors: Michał Dębski, Zbigniew Lonc, Karolina Okrasa, Marta Piecyk, and Paweł Rzążewski

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
For graphs G and H, an H-coloring of G is an edge-preserving mapping from V(G) to V(H). In the H-Coloring problem the graph H is fixed and we ask whether an instance graph G admits an H-coloring. A generalization of this problem is H-ColoringExt, where some vertices of G are already mapped to vertices of H and we ask if this partial mapping can be extended to an H-coloring. We study the complexity of variants of H-Coloring in F-free graphs, i.e., graphs excluding a fixed graph F as an induced subgraph. For integers a,b,c ⩾ 1, by S_{a,b,c} we denote the graph obtained by identifying one endvertex of three paths on a+1, b+1, and c+1 vertices, respectively. For odd k ⩾ 5, by W_k we denote the graph obtained from the k-cycle by adding a universal vertex. As our main algorithmic result we show that W_5-ColoringExt is polynomial-time solvable in S_{2,1,1}-free graphs. This result exhibits an interesting non-monotonicity of H-ColoringExt with respect to taking induced subgraphs of H. Indeed, W_5 contains a triangle, and K_3-Coloring, i.e., classical 3-coloring, is NP-hard already in claw-free (i.e., S_{1,1,1}-free) graphs. Our algorithm is based on two main observations: 1) W_5-ColoringExt in S_{2,1,1}-free graphs can be in polynomial time reduced to a variant of the problem of finding an independent set intersecting all triangles, and 2) the latter problem can be solved in polynomial time in S_{2,1,1}-free graphs. We complement this algorithmic result with several negative ones. In particular, we show that W_5-Coloring is NP-hard in P_t-free graphs for some constant t and W_5-ColoringExt is NP-hard in S_{3,3,3}-free graphs of bounded degree. This is again uncommon, as usually problems that are NP-hard in S_{a,b,c}-free graphs for some constant a,b,c are already hard in claw-free graphs
Cite as

Michał Dębski, Zbigniew Lonc, Karolina Okrasa, Marta Piecyk, and Paweł Rzążewski. Computing Homomorphisms in Hereditary Graph Classes: The Peculiar Case of the 5-Wheel and Graphs with No Long Claws. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{debski_et_al:LIPIcs.ISAAC.2022.14,
  author =	{D\k{e}bski, Micha{\l} and Lonc, Zbigniew and Okrasa, Karolina and Piecyk, Marta and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Computing Homomorphisms in Hereditary Graph Classes: The Peculiar Case of the 5-Wheel and Graphs with No Long Claws}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.14},
  URN =		{urn:nbn:de:0030-drops-172996},
  doi =		{10.4230/LIPIcs.ISAAC.2022.14},
  annote =	{Keywords: graph homomorphism, forbidden induced subgraphs, precoloring extension}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.37
Faster 3-Coloring of Small-Diameter Graphs

Authors: Michał Dębski, Marta Piecyk, and Paweł Rzążewski

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We study the 3-Coloring problem in graphs with small diameter. In 2013, Mertzios and Spirakis showed that for n-vertex diameter-2 graphs this problem can be solved in subexponential time 2^{𝒪(√{n log n})}. Whether the problem can be solved in polynomial time remains a well-known open question in the area of algorithmic graphs theory. In this paper we present an algorithm that solves 3-Coloring in n-vertex diameter-2 graphs in time 2^{𝒪(n^{1/3} log² n)}. This is the first improvement upon the algorithm of Mertzios and Spirakis in the general case, i.e., without putting any further restrictions on the instance graph. In addition to standard branchings and reducing the problem to an instance of 2-Sat, the crucial building block of our algorithm is a combinatorial observation about 3-colorable diameter-2 graphs, which is proven using a probabilistic argument. As a side result, we show that 3-Coloring can be solved in time 2^{𝒪((n log n)^{2/3})} in n-vertex diameter-3 graphs. We also generalize our algorithms to the problem of finding a list homomorphism from a small-diameter graph to a cycle.
Cite as

Michał Dębski, Marta Piecyk, and Paweł Rzążewski. Faster 3-Coloring of Small-Diameter Graphs. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{debski_et_al:LIPIcs.ESA.2021.37,
  author =	{D\k{e}bski, Micha{\l} and Piecyk, Marta and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Faster 3-Coloring of Small-Diameter Graphs}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.37},
  URN =		{urn:nbn:de:0030-drops-146181},
  doi =		{10.4230/LIPIcs.ESA.2021.37},
  annote =	{Keywords: 3-coloring, fine-grained complexity, subexponential-time algorithm, diameter}
}
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