5 Search Results for "Babenko, Maxim"

Document
DOI: 10.4230/LIPIcs.ESA.2025.72
Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions

Authors: Noam Horowicz and Tsvi Kopelowitz

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In the snippets problem, the goal is to preprocess a text T so that given two pattern queries, P₁ and P₂, one can quickly locate the occurrences of the two patterns in T that are closest to each other, or report the distance between these occurrences. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that preprocess a set of points with associated colors so that given two colors c and c' one can quickly find the (distance between the) closest pair of points where one has color c and the other has color c'. However, the existing upper bound and lower bound curves are not tight. Inspired by recent advances by Kopelowitz and Vassilevska-Williams [ICALP2020] regarding tradeoff curves for Set-disjointness data structures, in this paper we introduce new conditionally optimal algorithms for a (1+ε) approximation version of the snippets problem and a (1+ε) approximation version of the CDO problem, by applying fast matrix multiplication. For example, for CDO on n points in an array, if the preprocessing time is Õ(n^a) and the query time is Õ(n^b) then, assuming that ω = 2 (where ω is the exponent of n in the runtime of the fastest matrix multiplication algorithm on two squared matrices of size n× n), we show that approximate CDO can be solved with the following tradeoff a + 2b = 2 (if 0 ≤ b ≤ 1/3) 2a + b = 3 (if 1/3 ≤ b ≤ 1). Moreover, we prove that for exact CDO on points in an array, the algorithm of Kopelowitz and Krauthgamer [CPM2016], which obtains a tradeoff of a+b = 2, is essentially optimal assuming that the strong all-pairs shortest paths hypothesis holds for randomized algorithms. Thus, we demonstrate that the exact version of CDO is strictly harder than the approximate version. Moreover, this separation carries over to the snippets problem.
Cite as

Noam Horowicz and Tsvi Kopelowitz. Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{horowicz_et_al:LIPIcs.ESA.2025.72,
  author =	{Horowicz, Noam and Kopelowitz, Tsvi},
  title =	{{Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{72:1--72:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.72},
  URN =		{urn:nbn:de:0030-drops-245403},
  doi =		{10.4230/LIPIcs.ESA.2025.72},
  annote =	{Keywords: data structures, fast matrix multiplication, fine-grained complexity, pattern matching, distance oracles}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
For a given graph G, a hopset H with hopbound β and stretch α is a set of edges such that between every pair of vertices u and v, there is a path with at most β hops in G ∪ H that approximates the distance between u and v up to a multiplicative stretch of α. Hopsets have found a wide range of applications for distance-based problems in various computational models since the 90s. More recently, there has been significant interest in understanding these fundamental objects from an existential and structural perspective. But all of this work takes a worst-case (or existential) point of view: How many edges do we need to add to satisfy a given hopbound and stretch requirement for any input graph? We initiate the study of the natural optimization variant of this problem: given a specific graph instance, what is the minimum number of edges that satisfy the hopbound and stretch requirements? We give approximation algorithms for a generalized hopset problem which, when combined with known existential bounds, lead to different approximation guarantees for various regimes depending on hopbound, stretch, and directed vs. undirected inputs. We complement our upper bounds with a lower bound that implies Label Cover hardness for directed hopsets and shortcut sets with hopbound at least 3.
Cite as

Michael Dinitz, Ama Koranteng, and Yasamin Nazari. Approximation Algorithms for Optimal Hopsets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.5
Packing Odd Walks and Trails in Multiterminal Networks

Authors: Maxim Akhmedov and Maxim Babenko

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Let G be an undirected network with a distinguished set of terminals T ⊆ V(G) and edge capacities cap: E(G) → ℝ_+. By an odd T-walk we mean a walk in G (with possible vertex and edge self-intersections) connecting two distinct terminals and consisting of an odd number of edges. Inspired by the work of Schrijver and Seymour on odd path packing for two terminals, we consider packings of odd T-walks subject to capacities cap. First, we present a strongly polynomial time algorithm for constructing a maximum fractional packing of odd T-walks. For even integer capacities, our algorithm constructs a packing that is half-integer. Additionally, if cap(δ(v)) is divisible by 4 for any v ∈ V(G)-T, our algorithm constructs an integer packing. Second, we establish and prove the corresponding min-max relation. Third, if G is inner Eulerian (i.e. degrees of all nodes in V(G)-T are even) and cap(e) = 2 for all e ∈ E, we show that there exists an integer packing of odd T-trails (i.e. odd T-walks with no repeated edges) of the same value as in case of odd T-walks, and this packing can be found in polynomial time. To achieve the above goals, we establish a connection between packings of odd T-walks and T-trails and certain multiflow problems in undirected and bidirected graphs.
Cite as

Maxim Akhmedov and Maxim Babenko. Packing Odd Walks and Trails in Multiterminal Networks. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{akhmedov_et_al:LIPIcs.STACS.2023.5,
  author =	{Akhmedov, Maxim and Babenko, Maxim},
  title =	{{Packing Odd Walks and Trails in Multiterminal Networks}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.5},
  URN =		{urn:nbn:de:0030-drops-176570},
  doi =		{10.4230/LIPIcs.STACS.2023.5},
  annote =	{Keywords: Odd path, signed and bidirected graph, multiflow, polynomial algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.8
Faster Algorithms for Half-Integral T-Path Packing

Authors: Maxim Babenko and Stepan Artamonov

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
Let G = (V, E) be an undirected graph, a subset of vertices T be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O(mn^1/2 log(n^2/m)/log(n))-time algorithm (hereinafter n := |V|, m := |E|). Now let us consider the fractional relaxation, i.e. allow T-path packings with arbitrary nonnegative real weights. It is known that there always exists a half-integral solution, that is, one only needs to assign weights 0, 1/2, 1 to maximize the total weight of T-paths. It is also known that an optimum half-integral packing can be found in strongly-polynomial time but the actual time bounds are far from being satisfactory. In this paper we present a novel algorithm that solves the half-integral problem within O(mn^1/2 log(n^2/m)/log(n)) time, thus matching the complexities of integral and half-integral versions.
Cite as

Maxim Babenko and Stepan Artamonov. Faster Algorithms for Half-Integral T-Path Packing. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 8:1-8:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{babenko_et_al:LIPIcs.ISAAC.2017.8,
  author =	{Babenko, Maxim and Artamonov, Stepan},
  title =	{{Faster Algorithms for Half-Integral T-Path Packing}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{8:1--8:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.8},
  URN =		{urn:nbn:de:0030-drops-82750},
  doi =		{10.4230/LIPIcs.ISAAC.2017.8},
  annote =	{Keywords: graph algorithms, multiflows, path packings, matchings}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.519
New Exact and Approximation Algorithms for the Star Packing Problem in Undirected Graphs

Authors: Maxim Babenko and Alexey Gusakov

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
By a T-star we mean a complete bipartite graph K_{1,t} for some t <= T. For an undirected graph G, a T-star packing is a collection of node-disjoint T-stars in G. For example, we get ordinary matchings for $T = 1$ and packings of paths of length 1 and 2 for $T = 2$. Hereinafter we assume that T >= 2. Hell and Kirkpatrick devised an ad-hoc augmenting algorithm that finds a T-star packing covering the maximum number of nodes. The latter algorithm also yields a min-max formula. We show that T-star packings are reducible to network flows, hence the above problem is solvable in $O(m sqrt(n))$ time (hereinafter n denotes the number of nodes in G, and m --- the number of edges). For the edge-weighted case (in which weights may be assumed positive) finding a maximum $T$-packing is NP-hard. A novel 9/4 T/(T + 1)-factor approximation algorithm is presented. For non-negative node weights the problem reduces to a special case of a max-cost flow. We develop a divide-and-conquer approach that solves it in O(m sqrt(n) log(n)) time. The node-weighted problem with arbitrary weights is more difficult. We prove that it is NP-hard for T >= 3 and is solvable in strongly-polynomial time for T = 2.
Cite as

Maxim Babenko and Alexey Gusakov. New Exact and Approximation Algorithms for the Star Packing Problem in Undirected Graphs. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 519-530, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

Copy BibTex To Clipboard

@InProceedings{babenko_et_al:LIPIcs.STACS.2011.519,
  author =	{Babenko, Maxim and Gusakov, Alexey},
  title =	{{New Exact and Approximation Algorithms for the Star Packing Problem in Undirected Graphs}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{519--530},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.519},
  URN =		{urn:nbn:de:0030-drops-30402},
  doi =		{10.4230/LIPIcs.STACS.2011.519},
  annote =	{Keywords: graph algorithms, approximation algorithms, generalized matchings, flows, weighted packings}
}
  • Refine by Type
  • 5 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2023
  • 1 2017
  • 1 2011

  • Refine by Author
  • 3 Babenko, Maxim
  • 1 Akhmedov, Maxim
  • 1 Artamonov, Stepan
  • 1 Dinitz, Michael
  • 1 Gusakov, Alexey
  • Show More...

  • Refine by Series/Journal
  • 5 LIPIcs

  • Refine by Classification
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Network optimization
  • 1 Theory of computation → Routing and network design problems

  • Refine by Keyword
  • 2 graph algorithms
  • 1 Approximation Algorithms
  • 1 Hopsets
  • 1 Odd path
  • 1 approximation algorithms
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact