21 Search Results for "Knop, Alexander"

Document
DOI: 10.4230/LIPIcs.CCC.2026.13
Resolution Width Lifts to Near-Quadratic-Depth Res(⊕) Size

Authors: Dmitry Itsykson, Vladimir Podolskii, and Alexander Shekhovtsov

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
We show that for any unsatisfiable CNF formula φ that requires resolution refutation width at least w, and for any 1-stifling gadget g (for example, g = MAJ₃), (1) every resolution-over-parities (Res(⊕)) refutation of the lifted formula φ∘g of size at most S has depth at least Ω(w²/log S); (2) every Res(⊕) refutation of the lifted formula φ∘g has size Ω(w²). The first result substantially extends and simplifies all previously known lifting theorems for bounded-depth Res(⊕). The lifting result of Itsykson and Knop [Dmitry Itsykson and Alexander Knop, 2026] requires gadgets of logarithmic size and applies only to refutations of depth at most O(nlog n), whereas our result applies to nearly quadratic depth. The liftings of Bhattacharya and Chattopadhyay [Sreejata Kishor Bhattacharya and Arkadev Chattopadhyay, 2025] and of Byramji and Impagliazzo [Farzan Byramji and Russell Impagliazzo, 2025] apply to nearly quadratic depth as well, but rely on a much stronger assumption of (Ω(n),Ω(n))-DT-hardness, which is far less standard than large resolution width. Our proof combines the random-walk-with-restarts method of Alekseev and Itsykson [Yaroslav Alekseev and Dmitry Itsykson, 2025] with a new idea: the random walk is defined relative to the structure of the refutation graph, rather than by a distribution on inputs induced by the formula. Using this technique, we substantially strengthen the supercritical size-depth tradeoff of Itsykson and Knop [Dmitry Itsykson and Alexander Knop, 2026], both by improving the depth lower bound and by reducing the size of the separating formulas to polynomial in the number of variables, with the latter resolving an open question posed in [Dmitry Itsykson and Alexander Knop, 2026]. In particular, we construct a family of polynomial-size formulas that admit polynomial-size resolution refutations, while any Res(⊕) refutation of depth o(n²/log⁴ n) necessarily has superpolynomial size. Our second result yields a pure quadratic lower bound on the size of Res(⊕) refutations, improving upon the previously known near-quadratic lower bound of [Farzan Byramji and Russell Impagliazzo, 2025].
Cite as

Dmitry Itsykson, Vladimir Podolskii, and Alexander Shekhovtsov. Resolution Width Lifts to Near-Quadratic-Depth Res(⊕) Size. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 13:1-13:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{itsykson_et_al:LIPIcs.CCC.2026.13,
  author =	{Itsykson, Dmitry and Podolskii, Vladimir and Shekhovtsov, Alexander},
  title =	{{Resolution Width Lifts to Near-Quadratic-Depth Res(⊕) Size}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{13:1--13:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.13},
  URN =		{urn:nbn:de:0030-drops-270558},
  doi =		{10.4230/LIPIcs.CCC.2026.13},
  annote =	{Keywords: lifting theorems, resolution depth, resolution over parities, resolution width, supercritical tradeoff, random walk with restarts}
}
Document
DOI: 10.4230/LIPIcs.FORC.2026.1
Computational Hardness of Private Coreset

Authors: Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract
We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 ± α) factor (and some additive factor). We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^{ω(1)})-DP algorithm can compute a coreset for k-means in the 𝓁_∞-metric for some constant α > 0 (and some constant additive factor), even for k = 3. For k-means in the Euclidean metric, we show a similar result but only for α = Θ(1/d²), where d is the dimension.
Cite as

Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi. Computational Hardness of Private Coreset. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghazi_et_al:LIPIcs.FORC.2026.1,
  author =	{Ghazi, Badih and Guzm\'{a}n, Crist\'{o}bal and Kamath, Pritish and Knop, Alexander and Kumar, Ravi and Manurangsi, Pasin},
  title =	{{Computational Hardness of Private Coreset}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.1},
  URN =		{urn:nbn:de:0030-drops-259725},
  doi =		{10.4230/LIPIcs.FORC.2026.1},
  annote =	{Keywords: Differentially Private Clustering, Coreset, Cryptographic Hardness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.51
Structural Parameterization of Steiner Tree Packing

Authors: Niko Hastrich and Kirill Simonov

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms. In this paper, we show the first FPT algorithms for STP parameterized by structural parameters of the input graph. In particular, we show that STP is fixed-parameter tractable by the tree-cut width as well as the fracture number of the input graph. To achieve our results, we generalize techniques from Edge-Disjoint Paths (EDP) to Generalized Steiner Tree Packing (GSTP), which generalizes both STP and EDP. First, we derive the notion of the augmented graph for GSTP analogous to EDP. We then show that GSTP is FPT by - the tree-cut width of the augmented graph, - the fracture number of the augmented graph, - the slim tree-cut width of the input graph. The latter two results were previously known for EDP; our results generalize these to GSTP and improve the running time for the parameter fracture number. On the other hand, it was open whether EDP is FPT parameterized by the tree-cut width of the augmented graph, despite extensive research on the structural complexity of the problem. We settle this question affirmatively.
Cite as

Niko Hastrich and Kirill Simonov. Structural Parameterization of Steiner Tree Packing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hastrich_et_al:LIPIcs.STACS.2026.51,
  author =	{Hastrich, Niko and Simonov, Kirill},
  title =	{{Structural Parameterization of Steiner Tree Packing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.51},
  URN =		{urn:nbn:de:0030-drops-255405},
  doi =		{10.4230/LIPIcs.STACS.2026.51},
  annote =	{Keywords: Steiner tree packing, structural parameters, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.23
Simple Circuit Extensions for XOR in PTIME

Authors: Marco Carmosino, Ngu Dang, and Tim Jackman

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The Minimum Circuit Size Problem for Partial Functions (MCSP^*) is hard assuming the Exponential Time Hypothesis (ETH) (Ilango, 2020). This breakthrough result leveraged a characterization of the optimal {∧, ∨, ¬} circuits for n-bit OR (OR_n) and a reduction from the partial f-Simple Extension Problem where f = OR_n. It remains open to extend that reduction to show ETH-hardness of total MCSP. However, Ilango observed that the total f-Simple Extension Problem is easy whenever f is computed by read-once formulas (like OR_n). Therefore, extending Ilango’s proof to total MCSP would require replacing OR_n with a more complex but similarly well-understood Boolean function. This work shows that the f-Simple Extension problem remains easy when f is the next natural candidate: XOR_n. We first develop a fixed-parameter tractable algorithm for the f-Simple Extension Problem that is efficient whenever the optimal circuits for f are (1) linear in size, (2) polynomially "few" and efficiently enumerable in the truth-table size (up to isomorphism and permutation of inputs), and (3) all have constant bounded fan-out. XOR_n satisfies all three of these conditions. When ¬ gates count towards circuit size, optimal XOR_n circuits are binary trees of n-1 subcircuits computing (¬)XOR₂ (Kombarov, 2011). We extend this characterization when ¬ gates do not contribute the circuit size. Thus, the XOR-Simple Extension Problem is in polynomial time under both measures of circuit complexity. We conclude by discussing conjectures about the complexity of the f-Simple Extension problem for each explicit function f with known and unrestricted circuit lower bounds over the DeMorgan basis. Examining the conditions under which our Simple Extension Solver is efficient, we argue that multiplexer functions (MUX) are the most promising candidate for ETH-hardness of a Simple Extension Problem, towards proving ETH-hardness of total MCSP.
Cite as

Marco Carmosino, Ngu Dang, and Tim Jackman. Simple Circuit Extensions for XOR in PTIME. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmosino_et_al:LIPIcs.STACS.2026.23,
  author =	{Carmosino, Marco and Dang, Ngu and Jackman, Tim},
  title =	{{Simple Circuit Extensions for XOR in PTIME}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.23},
  URN =		{urn:nbn:de:0030-drops-255127},
  doi =		{10.4230/LIPIcs.STACS.2026.23},
  annote =	{Keywords: Minimum Circuit Size Problem, Circuit Lower Bounds, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.81
Supercritical Tradeoff Between Size and Depth for Resolution over Parities

Authors: Dmitry Itsykson and Alexander Knop

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Alekseev and Itsykson (STOC 2025) proved the existence of an unsatisfiable CNF formula such that any resolution over parities (Res(⊕)) refutation must either have exponential size (in the formula size) or superlinear depth (in the number of variables). In this paper, we extend this result by constructing a formula with the same hardness properties, but which additionally admits a resolution refutation of quasi-polynomial size. This establishes a supercritical tradeoff between size and depth for resolution over parities. The proof builds on the framework of Alekseev and Itsykson and relies on a lifting argument applied to the supercritical tradeoff between width and depth in resolution, proposed by Buss and Thapen (IPL 2026).
Cite as

Dmitry Itsykson and Alexander Knop. Supercritical Tradeoff Between Size and Depth for Resolution over Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{itsykson_et_al:LIPIcs.ITCS.2026.81,
  author =	{Itsykson, Dmitry and Knop, Alexander},
  title =	{{Supercritical Tradeoff Between Size and Depth for Resolution over Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{81:1--81:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.81},
  URN =		{urn:nbn:de:0030-drops-253680},
  doi =		{10.4230/LIPIcs.ITCS.2026.81},
  annote =	{Keywords: lifting theorems, resolution depth, resolution over parities, resolution width, supercritical tradeoff}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
Cite as

Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
Cite as

Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.15
Parameterized Complexity of Directed Traveling Salesman Problem

Authors: Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed walk of minimum length (or total weight) that visits every vertex of the given graph at least once. In a yet more general version, Directed Waypoint Routing Problem (DWRP), some vertices are marked as terminals and we are only required to visit all terminals. Furthermore, each edge has its capacity bounding the number of times this edge can be used by a solution. While both problems (and many other variants of TSP) were extensively investigated, mostly from the approximation point of view, there are surprisingly few results concerning the parameterized complexity. Our starting point is the result of Marx et al. [APPROX/RANDOM 2016] who proved that DTSP is W[1]-hard parameterized by distance to pathwidth 3. In this paper we aim to initiate the systematic complexity study of variants of Directed Traveling Salesman Problem with respect to various, mostly structural, parameters. We show that DWRP is FPT parameterized by the solution size, the feedback edge number and the vertex integrity of the underlying undirected graph. Furthermore, the problem is XP parameterized by treewidth. On the complexity side, we show that the problem is W[1]-hard parameterized by the distance to constant treedepth.
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Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý. Parameterized Complexity of Directed Traveling Salesman Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.ISAAC.2025.15,
  author =	{Bla\v{z}ej, V\'{a}clav and Feldmann, Andreas Emil and Fioravantes, Foivos and Rz\k{a}\.{z}ewski, Pawe{\l} and Such\'{y}, Ond\v{r}ej},
  title =	{{Parameterized Complexity of Directed Traveling Salesman Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.15},
  URN =		{urn:nbn:de:0030-drops-249231},
  doi =		{10.4230/LIPIcs.ISAAC.2025.15},
  annote =	{Keywords: Directed TSP, parameterized complexity, vertex integrity, treedepth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.15
Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors: Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan

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

Abstract
In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems: 1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components. 2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.
Cite as

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ESA.2025.15,
  author =	{Depian, Thomas and Fink, Simon D. and Ganian, Robert and Surianarayanan, Vaishali},
  title =	{{Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-244835},
  doi =		{10.4230/LIPIcs.ESA.2025.15},
  annote =	{Keywords: stack layouts, queue layouts, parameterized algorithms, vertex integrity, Ramsey theory}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.32
Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems

Authors: Niels Grüttemeier, Nils Morawietz, and Frank Sommer

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

Abstract
Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution, the parameterized approach aims to improve a solution by performing k simultaneous operations. Herein, k is a parameter called search radius for which the value can be chosen by a user. One major goal in the field of parameterized local search is to outline the trade-off between the size of k and the running time of the local search step. In this work, we introduce an abstract framework that generalizes natural parameterized local search approaches for a large class of partitioning problems: Given n items that are partitioned into b bins and a target function that evaluates the quality of the current partition, one asks whether it is possible to improve the solution by removing up to k items from their current bins and reassigning them to other bins. Among others, our framework applies for the local search versions of problems like Cluster Editing, Vector Bin Packing, and Nash Social Welfare. Motivated by a real-world application of the problem Vector Bin Packing, we introduce a parameter called number of types τ ≤ n and show that all problems fitting in our framework can be solved in τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) time, where |I| denotes the total input size. In case of Cluster Editing, the parameter τ generalizes the well-known parameter neighborhood diversity of the input graph. We complement these algorithms by showing that for all considered problems, an algorithm significantly improving over our algorithm with running time τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) would contradict the Exponential Time Hypothesis. Additionally, we show that even on very restricted instances, all considered problems are W[1]-hard when parameterized by the search radius k alone. In case of the local search version of Vector Bin Packing, we provide an even stronger W[1]-hardness result.
Cite as

Niels Grüttemeier, Nils Morawietz, and Frank Sommer. Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gruttemeier_et_al:LIPIcs.WADS.2025.32,
  author =	{Gr\"{u}ttemeier, Niels and Morawietz, Nils and Sommer, Frank},
  title =	{{Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{32:1--32:20},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-242631},
  doi =		{10.4230/LIPIcs.WADS.2025.32},
  annote =	{Keywords: Flip-Neighborhood, Cluster Editing, Vector Bin Packing, Vertex Cover, NP-hard problem, Max c-Cut}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.8
Amortized Closure and Its Applications in Lifting for Resolution over Parities

Authors: Klim Efremenko and Dmitry Itsykson

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The notion of closure of a set of linear forms, first introduced by Efremenko, Garlik, and Itsykson [Klim Efremenko et al., 2024], has proven instrumental in proving lower bounds on the sizes of regular and bounded-depth Res(⊕) refutations [Klim Efremenko et al., 2024; Yaroslav Alekseev and Dmitry Itsykson, 2025]. In this work, we present amortized closure, an enhancement that retains the properties of original closure [Klim Efremenko et al., 2024] but offers tighter control on its growth. Specifically, adding a new linear form increases the amortized closure by at most one. We explore two applications that highlight the power of this new concept. Utilizing our newly defined amortized closure, we extend and provide a succinct and elegant proof of the recent lifting theorem by Chattopadhyay and Dvorak [Arkadev Chattopadhyay and Pavel Dvorak, 2025]. Namely we show that for an unsatisfiable CNF formula φ and a 1-stifling gadget g: {0,1}^𝓁 → {0,1}, if the lifted formula φ∘g has a tree-like Res(⊕) refutation of size 2^d and width w, then φ has a resolution refutation of depth d and width w. The original theorem by Chattopadhyay and Dvorak [Arkadev Chattopadhyay and Pavel Dvorak, 2025] applies only to the more restrictive class of strongly stifling gadgets. As a more significant application of amortized closure, we show improved lower bounds for bounded-depth Res(⊕), extending the depth beyond that of Alekseev and Itsykson [Yaroslav Alekseev and Dmitry Itsykson, 2025]. Our result establishes an exponential lower bound for depth-Ω(n log n) Res(⊕) refutations of lifted Tseitin formulas, a notable improvement over the existing depth-Ω(n log log n) Res(⊕) lower bound.
Cite as

Klim Efremenko and Dmitry Itsykson. Amortized Closure and Its Applications in Lifting for Resolution over Parities. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{efremenko_et_al:LIPIcs.CCC.2025.8,
  author =	{Efremenko, Klim and Itsykson, Dmitry},
  title =	{{Amortized Closure and Its Applications in Lifting for Resolution over Parities}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{8:1--8:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.8},
  URN =		{urn:nbn:de:0030-drops-237023},
  doi =		{10.4230/LIPIcs.CCC.2025.8},
  annote =	{Keywords: lifting, resolution over parities, closure of linear forms, lower bounds, width, depth, size vs depth tradeoff}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.16
Direct Sums for Parity Decision Trees

Authors: Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Direct sum theorems state that the cost of solving k instances of a problem is at least Ω(k) times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.
Cite as

Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan. Direct Sums for Parity Decision Trees. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 16:1-16:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{besselman_et_al:LIPIcs.CCC.2025.16,
  author =	{Besselman, Tyler and G\"{o}\"{o}s, Mika and Guo, Siyao and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{Direct Sums for Parity Decision Trees}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{16:1--16:38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.16},
  URN =		{urn:nbn:de:0030-drops-237105},
  doi =		{10.4230/LIPIcs.CCC.2025.16},
  annote =	{Keywords: direct sum, parity decision trees, query complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.112
Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns

Authors: Alexandra Lassota and Koen Ligthart

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

Abstract
We study integer linear programs (ILP) of the form min{c^⊤ x | Ax = b,l ≤ x ≤ u,x ∈ ℤⁿ} and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the well-established approach of capturing the hardness of a problem by the distance to triviality. The generalized matching problem is an ILP where each column of the constraint matrix has 1-norm of at most 2. It captures several well-known polynomial time solvable problems such as matching and flow problems. We parameterize by the size of variable and constraint backdoors, which measure the least number of columns or rows that must be deleted to obtain a generalized matching ILP. This extends generalized matching problems by allowing a parameterized number of additional arbitrary variables or constraints, yielding a novel parameter. We present the following results: (i) a fixed-parameter tractable (FPT) algorithm for ILPs parameterized by the size p of a minimum variable backdoor to generalized matching; (ii) a randomized slice-wise polynomial (XP) time algorithm for ILPs parameterized by the size h of a minimum constraint backdoor to generalized matching as long as c and A are encoded in unary; (iii) we complement (ii) by proving that solving an ILP is W[1]-hard when parameterized by h even when c,A,l,u have coefficients of constant size. To obtain (i), we prove a variant of lattice-convexity of the degree sequences of weighted b-matchings, which we study in the light of SBO jump M-convex functions. This allows us to model the matching part as a polyhedral constraint on the integer backdoor variables. The resulting ILP is solved in FPT time using an integer programming algorithm. For (ii), the randomized XP time algorithm is obtained by pseudo-polynomially reducing the problem to the exact matching problem. To prevent an exponential blowup in terms of the encoding length of b, we bound the Graver complexity of the constraint matrix and employ a Graver augmentation local search framework. The hardness result (iii) is obtained through a parameterized reduction from ILP with h constraints and coefficients encoded in unary.
Cite as

Alexandra Lassota and Koen Ligthart. Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 112:1-112:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lassota_et_al:LIPIcs.ICALP.2025.112,
  author =	{Lassota, Alexandra and Ligthart, Koen},
  title =	{{Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{112:1--112:18},
  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.2025.112},
  URN =		{urn:nbn:de:0030-drops-234895},
  doi =		{10.4230/LIPIcs.ICALP.2025.112},
  annote =	{Keywords: Integer Programming, fixed-parameter Tractability, polyhedral Optimization, Matchings}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.17
Branching Programs with Bounded Repetitions and Flow Formulas

Authors: Anastasia Sofronova and Dmitry Sokolov

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
Restricted branching programs capture various complexity measures like space in Turing machines or length of proofs in proof systems. In this paper, we focus on the application in the proof complexity that was discovered by Lovasz et al. [László Lovász et al., 1995] who showed the equivalence between regular Resolution and read-once branching programs for "unsatisfied clause search problem" (Search_φ). This connection is widely used, in particular, in the recent breakthrough result about the Clique problem in regular Resolution by Atserias et al. [Albert Atserias et al., 2018]. We study the branching programs with bounded repetitions, so-called (1,+k)-BPs (Sieling [Detlef Sieling, 1996]) in application to the Search_φ problem. On the one hand, it is a natural generalization of read-once branching programs. On the other hand, this model gives a powerful proof system that can efficiently certify the unsatisfiability of a wide class of formulas that is hard for Resolution (Knop [Alexander Knop, 2017]). We deal with Search_φ that is "relatively easy" compared to all known hard examples for the (1,+k)-BPs. We introduce the first technique for proving exponential lower bounds for the (1,+k)-BPs on Search_φ. To do it we combine a well-known technique for proving lower bounds on the size of branching programs [Detlef Sieling, 1996; Detlef Sieling and Ingo Wegener, 1994; Stasys Jukna and Alexander A. Razborov, 1998] with the modification of the "closure" technique [Michael Alekhnovich et al., 2004; Michael Alekhnovich and Alexander A. Razborov, 2003]. In contrast with most Resolution lower bounds, our technique uses not only "local" properties of the formula, but also a "global" structure. Our hard examples are based on the Flow formulas introduced in [Michael Alekhnovich and Alexander A. Razborov, 2003].
Cite as

Anastasia Sofronova and Dmitry Sokolov. Branching Programs with Bounded Repetitions and Flow Formulas. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sofronova_et_al:LIPIcs.CCC.2021.17,
  author =	{Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Branching Programs with Bounded Repetitions and Flow Formulas}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{17:1--17:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.17},
  URN =		{urn:nbn:de:0030-drops-142915},
  doi =		{10.4230/LIPIcs.CCC.2021.17},
  annote =	{Keywords: proof complexity, branching programs, bounded repetitions, lower bounds}
}
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