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Documents authored by Lachish, Oded

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.15
Testing C_k-Freeness in Bounded Admissibility Graphs

Authors: Christine Awofeso, Patrick Greaves, Oded Lachish, Amit Levi, and Felix Reidl

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

Abstract
We study C_k-freeness in sparse graphs from a property testing perspective, specifically for graph classes with bounded r-admissibility. Our work is motivated by the large gap between upper and lower bounds in this area: C_k-freeness is known to be testable in planar graphs [Czumaj and Sohler, 2019], but not in graphs with bounded arboricity for k > 3 [Talya Eden et al., 2024]. There are a large number of interesting graph classes that include planar graphs and have bounded arboricity (e.g. classes excluding a minor), calling for a more fine-grained approach to the question of testing C_k-freeness in sparse graph classes. One such approach, inspired by the work of Nesetril and Ossona de Mendez [Nešetřil and {Ossona de Mendez}, 2012], is to consider the graph measure of r-admissibility, which naturally forms a hierarchy of graph families A₁ ⊃ A₂ ⊃ … ⊃ A_∞ where A_r contains all graph classes whose r-admissibility is bounded by some constant. The family A₁ contains classes with bounded arboricity, the class A_∞ contains classes like planar graphs, graphs of bounded degree, and minor-free graphs. Awofeso ηl [Awofeso et al., 2025] recently made progress in this direction. They showed that C₄- and C₅-freeness is testable in A₂. They further showed that C_k-freeness is not testable in A_{⌊k/2⌋ -1} and conjectured that C_k-freeness is testable in A_{⌊k/2⌋}. In this work, we prove this conjecture: C_k-freeness is indeed testable in graphs of bounded ⌊k/2⌋-admissibility.
Cite as

Christine Awofeso, Patrick Greaves, Oded Lachish, Amit Levi, and Felix Reidl. Testing C_k-Freeness in Bounded Admissibility Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{awofeso_et_al:LIPIcs.ICALP.2025.15,
  author =	{Awofeso, Christine and Greaves, Patrick and Lachish, Oded and Levi, Amit and Reidl, Felix},
  title =	{{Testing C\underlinek-Freeness in Bounded Admissibility Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{15:1--15:20},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-233926},
  doi =		{10.4230/LIPIcs.ICALP.2025.15},
  annote =	{Keywords: Property Testing, Sparse Graphs, Cycle, Admissibility}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.12
Shortest Undirected Paths in de Bruijn Graphs

Authors: Wiktor Zuba, Oded Lachish, and Solon P. Pissis

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Computing shortest directed paths in de Bruijn graphs is well studied and well understood. This is not the case for computing undirected paths, which is much more challenging algorithmically. In this paper, we present a general framework for computing shortest undirected paths in arbitrary de Bruijn graphs, that is, arbitrary subgraphs of the complete de Bruijn graph. We then present an application of our techniques for making any arbitrary order-k de Bruijn graph G(V,E) weakly connected by adding a set of edges of minimum total cost. This improves the running time of the recent (2-2/d)-approximation algorithm by Bernardini et al. [CPM 2024] from 𝒪(k|V|²) to 𝒪(k|V|log d) time, where d is the number of weakly connected components of graph G.
Cite as

Wiktor Zuba, Oded Lachish, and Solon P. Pissis. Shortest Undirected Paths in de Bruijn Graphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zuba_et_al:LIPIcs.CPM.2025.12,
  author =	{Zuba, Wiktor and Lachish, Oded and Pissis, Solon P.},
  title =	{{Shortest Undirected Paths in de Bruijn Graphs}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{12:1--12:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.12},
  URN =		{urn:nbn:de:0030-drops-231060},
  doi =		{10.4230/LIPIcs.CPM.2025.12},
  annote =	{Keywords: string algorithm, graph algorithm, de Bruijn graph, Eulerian graph}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.12
Results on H-Freeness Testing in Graphs of Bounded r-Admissibility

Authors: Christine Awofeso, Patrick Greaves, Oded Lachish, and Felix Reidl

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We study the property of H-freeness in graphs with known bounded average degree, i.e. the property of a graph not containing some graph H as a subgraph. H-freeness is one of the fundamental graph properties that has been studied in the property testing framework. Levi [Reut Levi, 2021] showed that triangle-freeness is testable in graphs of bounded arboricity, which is a superset of e.g. planar graphs or graphs of bounded degree. Complementing this result is a recent preprint [Talya Eden et al., 2024] by Eden ηl which shows that, for every r ≥ 4, C_r-freeness is not testable in graphs of bounded arboricity. We proceed in this line of research by using the r-admissibility measure that originates from the field of structural sparse graph theory. Graphs of bounded 1-admissibility are identical to graphs of bounded arboricity, while graphs of bounded degree, planar graphs, graphs of bounded genus, and even graphs excluding a fixed graph as a (topological) minor have bounded r-admissibility for any value of r [Nešetřil and Ossona de Mendez, 2012]. In this work we show that H-freeness is testable in graphs with bounded 2-admissibility for all graphs H of diameter 2. Furthermore, we show the testability of C₄-freeness in bounded 2-admissible graphs directly (with better query complexity) and extend this result to C₅-freeness. Using our techniques it is also possible to show that C₆-freeness and C₇-freeness are testable in graphs with bounded 3-admissibility. The formal proofs will appear in the journal version of this paper. These positive results are supplemented with a lower bound showing that, for every r ≥ 4, C_r-freeness is not testable for graphs of bounded (⌊r/2⌋ - 1)-admissibility. This lower bound will appear in the journal version of this paper. This implies that, for every r > 0, there exists a graph H of diameter r+1, such that H-freeness is not testable on graphs with bounded r-admissibility. These results lead us to the conjecture that, for every r > 4, and t ≤ 2r+1, C_t-freeness is testable in graphs of bounded r-admissibility, and for every r > 2, H-freeness for graphs H of diameter r is testable in graphs with bounded r-admissibility.
Cite as

Christine Awofeso, Patrick Greaves, Oded Lachish, and Felix Reidl. Results on H-Freeness Testing in Graphs of Bounded r-Admissibility. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{awofeso_et_al:LIPIcs.STACS.2025.12,
  author =	{Awofeso, Christine and Greaves, Patrick and Lachish, Oded and Reidl, Felix},
  title =	{{Results on H-Freeness Testing in Graphs of Bounded r-Admissibility}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.12},
  URN =		{urn:nbn:de:0030-drops-228378},
  doi =		{10.4230/LIPIcs.STACS.2025.12},
  annote =	{Keywords: Property Testing, Sparse Graphs, Degeneracy, Admissibility}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.25
When You Come at the King You Best Not Miss

Authors: Oded Lachish, Felix Reidl, and Chhaya Trehan

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
A tournament is an orientation of a complete graph. We say that a vertex x in a tournament T controls another vertex y if there exists a directed path of length at most two from x to y. A vertex is called a king if it controls every vertex of the tournament. It is well known that every tournament has a king. We follow Shen, Sheng, and Wu [Jian Shen et al., 2003] in investigating the query complexity of finding a king, that is, the number of arcs in T one has to know in order to surely identify at least one vertex as a king. The aforementioned authors showed that one always has to query at least Ω(n^{4/3}) arcs and provided a strategy that queries at most O(n^{3/2}). While this upper bound has not yet been improved for the original problem, [Biswas et al., 2017] proved that with O(n^{4/3}) queries one can identify a semi-king, meaning a vertex which controls at least half of all vertices. Our contribution is a novel strategy which improves upon the number of controlled vertices: using O(n^{4/3} polylog n) queries, we can identify a (1/2+2/17)-king. To achieve this goal we use a novel structural result for tournaments.
Cite as

Oded Lachish, Felix Reidl, and Chhaya Trehan. When You Come at the King You Best Not Miss. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 25:1-25:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lachish_et_al:LIPIcs.FSTTCS.2022.25,
  author =	{Lachish, Oded and Reidl, Felix and Trehan, Chhaya},
  title =	{{When You Come at the King You Best Not Miss}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{25:1--25:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.25},
  URN =		{urn:nbn:de:0030-drops-174177},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.25},
  annote =	{Keywords: Digraphs, tournaments, kings, query complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.31
Improving and Extending the Testing of Distributions for Shape-Restricted Properties

Authors: Eldar Fischer, Oded Lachish, and Yadu Vasudev

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Distribution testing deals with what information can be deduced about an unknown distribution over {1,...,n}, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In the extended conditional sampling model, the algorithm is also allowed to obtain samples from the restriction of the original distribution on subsets of {1,...,n}. In 2015, Canonne, Diakonikolas, Gouleakis and Rubinfeld unified several previous results, and showed that for any property of distributions satisfying a "decomposability" criterion, there exists an algorithm (in the basic model) that can distinguish with high probability distributions satisfying the property from distributions that are far from it in variation distance. We present here a more efficient yet simpler algorithm for the basic model, as well as very efficient algorithms for the conditional model, which until now was not investigated under the umbrella of decomposable properties. Additionally, we provide an algorithm for the conditional model that handles a much larger class of properties. Our core mechanism is a way of efficiently producing an interval-partition of {1,...,n} that satisfies a "fine-grain" quality. We show that with such a partition at hand we can directly move forward with testing individual intervals, instead of first searching for the "correct" partition of {1,...,n}.
Cite as

Eldar Fischer, Oded Lachish, and Yadu Vasudev. Improving and Extending the Testing of Distributions for Shape-Restricted Properties. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{fischer_et_al:LIPIcs.STACS.2017.31,
  author =	{Fischer, Eldar and Lachish, Oded and Vasudev, Yadu},
  title =	{{Improving and Extending the Testing of Distributions for Shape-Restricted Properties}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.31},
  URN =		{urn:nbn:de:0030-drops-70024},
  doi =		{10.4230/LIPIcs.STACS.2017.31},
  annote =	{Keywords: conditional sampling, distribution testing, property testing, statistics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2452
Two-phase Algorithms for the Parametric Shortest Path Problem

Authors: Sourav Chakraborty, Eldar Fischer, Oded Lachish, and Raphael Yuster

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
A {\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph problems are generalizations of weighted graph problems, and arise in various natural scenarios. Parametric weighted graph algorithms consist of two phases. A {\em preprocessing phase} whose input is a parametric weighted graph, and whose output is a data structure, the advice, that is later used by the {\em instantiation phase}, where a specific value for the variable is given. The instantiation phase outputs the solution to the (standard) weighted graph problem that arises from the instantiation. The goal is to have the running time of the instantiation phase supersede the running time of any algorithm that solves the weighted graph problem from scratch, by taking advantage of the advice. In this paper we construct several parametric algorithms for the shortest path problem. For the case of linear function weights we present an algorithm for the single source shortest path problem. Its preprocessing phase runs in $\tilde{O}(V^4)$ time, while its instantiation phase runs in only $O(E+V \log V)$ time. The fastest standard algorithm for single source shortest path runs in $O(VE)$ time. For the case of weight functions defined by degree $d$ polynomials, we present an algorithm with quasi-polynomial preprocessing time $O(V^{(1 + \log f(d))\log V})$ and instantiation time only $\tilde{O}(V)$. In fact, for any pair of vertices $u,v$, the instantiation phase computes the distance from $u$ to $v$ in only $O(\log^2 V)$ time. Finally, for linear function weights, we present a randomized algorithm whose preprocessing time is $\tilde{O (V^{3.5})$ and so that for any pair of vertices $u,v$ and any instantiation variable, the instantiation phase computes, in $O(1)$ time, a length of a path from $u$ to $v$ that is at most (additively) $\epsilon$ larger than the length of a shortest path. In particular, an all-pairs shortest path solution, up to an additive constant error, can be computed in $O(V^2)$ time.
Cite as

Sourav Chakraborty, Eldar Fischer, Oded Lachish, and Raphael Yuster. Two-phase Algorithms for the Parametric Shortest Path Problem. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 167-178, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chakraborty_et_al:LIPIcs.STACS.2010.2452,
  author =	{Chakraborty, Sourav and Fischer, Eldar and Lachish, Oded and Yuster, Raphael},
  title =	{{Two-phase Algorithms for the Parametric Shortest Path Problem}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{167--178},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2452},
  URN =		{urn:nbn:de:0030-drops-24523},
  doi =		{10.4230/LIPIcs.STACS.2010.2452},
  annote =	{Keywords: Parametric Algorithms, Shortest path problem}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2009.2317
The Covering and Boundedness Problems for Branching Vector Addition Systems

Authors: Stéphane Demri, Marcin Jurdzinski, Oded Lachish, and Ranko Lazic

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
The covering and boundedness problems for branching vector addition systems are shown complete for doubly-exponential time.
Cite as

Stéphane Demri, Marcin Jurdzinski, Oded Lachish, and Ranko Lazic. The Covering and Boundedness Problems for Branching Vector Addition Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{demri_et_al:LIPIcs.FSTTCS.2009.2317,
  author =	{Demri, St\'{e}phane and Jurdzinski, Marcin and Lachish, Oded and Lazic, Ranko},
  title =	{{The Covering and Boundedness Problems for Branching Vector Addition Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{181--192},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2317},
  URN =		{urn:nbn:de:0030-drops-23173},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2317},
  annote =	{Keywords: Vector addition systems, Petri nets, covering, boundedness, computational complexity}
}
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