23 Search Results for "Savani, Rahul"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.19
Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements

Authors: Michaela Borzechowski, Sebastian Haslebacher, Hung P. Hoang, Patrick Schnider, and Simon Weber

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
The famous Ham-Sandwich theorem states that any d point sets in ℝ^d can be simultaneously bisected by a single hyperplane. The α-Ham-Sandwich theorem gives a sufficient condition for the existence of biased cuts, i.e., hyperplanes that do not cut off half but some prescribed fraction of each point set. We give two new proofs for this theorem. The first proof is completely combinatorial and highlights a strong connection between the α-Ham-Sandwich theorem and Unique Sink Orientations of grids. The second proof uses point-hyperplane duality and the Poincaré-Miranda theorem and allows us to generalize the result to and beyond oriented matroids. For this we introduce a new concept of rainbow arrangements, generalizing colored pseudo-hyperplane arrangements. Along the way, we also show that the realizability problem for rainbow arrangements is ∃ℝ-complete, which also implies that the realizability problem for grid Unique Sink Orientations is ∃ℝ-complete.
Cite as

Michaela Borzechowski, Sebastian Haslebacher, Hung P. Hoang, Patrick Schnider, and Simon Weber. Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{borzechowski_et_al:LIPIcs.SoCG.2026.19,
  author =	{Borzechowski, Michaela and Haslebacher, Sebastian and Hoang, Hung P. and Schnider, Patrick and Weber, Simon},
  title =	{{Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.19},
  URN =		{urn:nbn:de:0030-drops-258250},
  doi =		{10.4230/LIPIcs.SoCG.2026.19},
  annote =	{Keywords: \alpha-Ham-Sandwich Theorem, Pseudo-Hyperplanes, Arrangements, Unique Sink Orientations, Oriented Matroids}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.19
Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level

Authors: Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
ARRIVAL is the problem of deciding whether a token, following a deterministic process, eventually reaches a designated destination. While the problem is known to lie in NP ∩ CoNP, whether it can be solved in polynomial time remains a major open question. In this article, we study ladders, a class of graphs that constitutes a family of worst-case instances for many existing algorithms, including the currently best known algorithm by Gärtner, Haslebacher, and Hoang (ICALP 2021). We show that ARRIVAL restricted to ladders can be solved in polynomial time, and we further extend this result to stopping binary simple stochastic games (SSG).
Cite as

Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang. Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{gartner_et_al:LIPIcs.FUN.2026.19,
  author =	{G\"{a}rtner, Bernd and Haslebacher, Sebastian and Hoang, Hung P.},
  title =	{{Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.19},
  URN =		{urn:nbn:de:0030-drops-257385},
  doi =		{10.4230/LIPIcs.FUN.2026.19},
  annote =	{Keywords: ARRIVAL, Rotor-Routing, Simple Stochastic Games}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.31
Lower Bounds for Ranking-Based Pivot Rules

Authors: Yann Disser, Georg Loho, Matthew Maat, and Nils Mosis

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

Abstract
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields. While numerous natural candidates for efficient rules have been eliminated, all existing lower bound constructions are tailored to individual or small sets of pivot rules. We introduce a unified framework for formalizing classes of rules according to the information about the input that they rely on. Within this framework, we show lower bounds for ranking-based classes of rules that base their decisions on orderings of the improving pivot steps induced by the underlying data. Our first result is a superpolynomial lower bound for strategy improvement, obtained via a family of sink parity games, which applies to memory-based generalizations of Bland’s rule that only access the input by comparing the ranks of improving edges in some global order. Our second result is a subexponential lower bound for policy iteration, obtained via a family of Markov decision processes, which applies to memoryless rules that only access the input by comparing improving actions according to their ranks in a global order, their reduced costs, and the associated improvements in objective value. Both results carry over to the simplex method for linear programming.
Cite as

Yann Disser, Georg Loho, Matthew Maat, and Nils Mosis. Lower Bounds for Ranking-Based Pivot Rules. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{disser_et_al:LIPIcs.STACS.2026.31,
  author =	{Disser, Yann and Loho, Georg and Maat, Matthew and Mosis, Nils},
  title =	{{Lower Bounds for Ranking-Based Pivot Rules}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{31:1--31:19},
  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.2026.31},
  URN =		{urn:nbn:de:0030-drops-255207},
  doi =		{10.4230/LIPIcs.STACS.2026.31},
  annote =	{Keywords: lower bounds, Markov decision processes, parity games, pivot rules, policy iteration, simplex method}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.59
When Is Local Search Both Effective and Efficient?

Authors: Artem Kaznatcheev and Sofia Vazquez Alferez

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

Abstract
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the "fitness" function to be maximized with the combinatorial structure of which assignments are "adjacent". Local search starts at an assignment in this landscape and successively moves assignments until no further improvement is possible among the adjacent assignments. Classic analyses of local search algorithms have focused more on the question of effectiveness ("did we find a good solution?") and often implicitly assumed that there are no doubts about their efficiency ("did we find it quickly?"). But there are many reasons to doubt the efficiency of local search. Even if we focus on fitness landscapes on the hypercube that are single peaked on every subcube (known as semismooth fitness landscapes, completely unimodal pseudo-Boolean functions, or acyclic unique sink orientations) where effectiveness is obvious, many local search algorithms are known to be inefficient. Since fitness landscapes are unwieldy exponentially large objects, we focus on their polynomial-sized representations by instances of valued constraint satisfaction problems (VCSP). We define a "direction" for valued constraints such that directed VCSPs generate semismooth fitness landscapes. We call directed VCSPs oriented if they do not have any pair of variables with arcs in both directions. Since recognizing if a VCSP-instance is directed or oriented is coNP-complete, we generalized oriented VCSPs as conditionally-smooth fitness landscapes where the structural property of "conditionally-smooth" is recognizable in polynomial time for a VCSP-instance. We prove that many popular local search algorithms like random ascent, simulated annealing, history-based rules, jumping rules, and the Kernighan-Lin heuristic are very efficient on conditionally-smooth landscapes. But conditionally-smooth landscapes are still expressive enough so that other well-regarded local search algorithms like steepest ascent and random facet require a super-polynomial number of steps to find the fitness peak.
Cite as

Artem Kaznatcheev and Sofia Vazquez Alferez. When Is Local Search Both Effective and Efficient?. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kaznatcheev_et_al:LIPIcs.STACS.2026.59,
  author =	{Kaznatcheev, Artem and Vazquez Alferez, Sofia},
  title =	{{When Is Local Search Both Effective and Efficient?}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{59:1--59:19},
  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.2026.59},
  URN =		{urn:nbn:de:0030-drops-255480},
  doi =		{10.4230/LIPIcs.STACS.2026.59},
  annote =	{Keywords: valued constraint satisfaction problem, local search, algorithm analysis, constraint graphs, pseudo-Boolean functions, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.52
Upper and Lower Bounds for the Linear Ordering Principle

Authors: Edward A. Hirsch and Ilya Volkovich

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

Abstract
Korten and Pitassi (FOCS, 2024) defined a new complexity class L₂^P as the polynomial-time Turing closure of the Linear Ordering Principle (a total function extending finding the minimum of an order [M. Chiari and J. Krajíček, 1998] to the case where the order is not linear). They put it between MA (Merlin-Arthur protocols) and S₂^P (the second symmetric level of the polynomial hierarchy). In this paper we sandwich L₂^P between P^prMA and P^prSBP. (The oracles here are promise problems, and SBP is the only known class between MA and AM.) The containment in P^prSBP is proved via an iterative process that uses a prSBP oracle to estimate the average order rank of a subset and find the minimum of a linear order. Another containment result of this paper is P^prO₂^P ⊆ O₂^P (where O₂^P is the input-oblivious version of S₂^P). These containment results altogether have several byproducts: - We give an affirmative answer to an open question posed by Chakaravarthy and Roy (Computational Complexity, 2011) whether P^prMA ⊆ S₂^P, thereby settling the relative standing of the existing (non-oblivious) Karp–Lipton–style collapse results of [V. T. Chakaravarthy and S. Roy, 2011] and [J.-Y. Cai, 2007], - We give an affirmative answer to an open question of Korten and Pitassi whether a Karp-Lipton-style collapse can be proven for L₂^P, - We show that the Karp-Lipton-style collapse to P^prOMA is actually better than both known collapses to P^prMA due to Chakaravarthy and Roy (Computational Complexity, 2011) and to O₂^P also due to Chakaravarthy and Roy (STACS, 2006). Thus we resolve the controversy between previously incomparable Karp-Lipton collapses stemming from these two lines of research.
Cite as

Edward A. Hirsch and Ilya Volkovich. Upper and Lower Bounds for the Linear Ordering Principle. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 52:1-52:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{hirsch_et_al:LIPIcs.STACS.2026.52,
  author =	{Hirsch, Edward A. and Volkovich, Ilya},
  title =	{{Upper and Lower Bounds for the Linear Ordering Principle}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{52:1--52:19},
  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.2026.52},
  URN =		{urn:nbn:de:0030-drops-255410},
  doi =		{10.4230/LIPIcs.STACS.2026.52},
  annote =	{Keywords: Complexity Classes, Structural Complexity Theory, Linear Ordering Principle, Symmetric Alternation, Merlin-Arthur Protocols, Karp-Lipton Collapse}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.14
Computing Tarski Fixed Points in Financial Networks

Authors: Leander Besting, Martin Hoefer, and Lars Huth

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

Abstract
Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model [Eisenberg and Noe, 2001], a fundamental aspect is clearing - to determine the amount of assets available to each financial institution in the presence of potential defaults and bankruptcy. A clearing state represents a fixed point that satisfies a set of natural axioms. Existence can be established (even in broad generalizations of the model) using Tarski’s theorem. While a maximal fixed point can be computed in polynomial time, the complexity of computing other fixed points is open. In this paper, we provide an efficient algorithm to compute a minimal fixed point. Our algorithm applies in a broad generalization of the Eisenberg-Noe model with any monotone, piecewise-linear payment functions and default costs. We also study claims trading, a local network adjustment to improve clearing, when networks are evaluated with minimal clearing. We provide an efficient algorithm to decide existence of Pareto-improving trades and compute optimal ones if they exist.
Cite as

Leander Besting, Martin Hoefer, and Lars Huth. Computing Tarski Fixed Points in Financial Networks. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{besting_et_al:LIPIcs.STACS.2026.14,
  author =	{Besting, Leander and Hoefer, Martin and Huth, Lars},
  title =	{{Computing Tarski Fixed Points in Financial Networks}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{14:1--14:18},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-255038},
  doi =		{10.4230/LIPIcs.STACS.2026.14},
  annote =	{Keywords: Tarski Fixed Points, Financial Networks, Minimal Clearing, Claims Trade}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.60
Total Search Problems in ZPP

Authors: Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan

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

Abstract
We initiate a systematic study of TFZPP, the class of total NP search problems solvable by polynomial time randomized algorithms. TFZPP contains a variety of important search problems such as Bertrand-Chebyshev (finding a prime between N and 2N), refuter problems for many circuit lower bounds, and Lossy-Code. The Lossy-Code problem has found prominence due to its fundamental connections to derandomization, catalytic computing, and the metamathematics of complexity theory, among other areas. While TFZPP collapses to FP under standard derandomization assumptions in the white-box setting, we are able to separate TFZPP from the major TFNP subclasses in the black-box setting. In fact, we are able to separate it from every uniform TFNP class assuming that NP is not in quasi-polynomial time. To do so, we extend the connection between proof complexity and black-box TFNP to randomized proof systems and randomized reductions. Next, we turn to developing a taxonomy of TFZPP problems. We highlight a problem called Nephew, originating from an infinity axiom in set theory. We show that Nephew is in PWPP∩ TFZPP and conjecture that it is not reducible to Lossy-Code. Intriguingly, except for some artificial examples, most other black-box TFZPP problems that we are aware of reduce to Lossy-Code: - We define a problem called Empty-Child capturing finding a leaf in a rooted (binary) tree, and show that this problem is equivalent to Lossy-Code. We also show that a variant of Empty-Child with "heights" is complete for the intersection of SOPL and Lossy-Code. - We strengthen Lossy-Code with several combinatorial inequalities such as the AM-GM inequality. Somewhat surprisingly, we show the resulting new problems are still reducible to Lossy-Code. A technical highlight of this result is that they are proved by formalizations in bounded arithmetic, specifically in Jeřábek’s theory APC₁ (JSL 2007). - Finally, we show that the Dense-Linear-Ordering problem reduces to Lossy-Code.
Cite as

Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan. Total Search Problems in ZPP. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 60:1-60:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{fleming_et_al:LIPIcs.ITCS.2026.60,
  author =	{Fleming, Noah and Grosser, Stefan and Jain, Siddhartha and Li, Jiawei and Ren, Hanlin and Shirley, Morgan and Yuan, Weiqiang},
  title =	{{Total Search Problems in ZPP}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{60:1--60:26},
  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.2026.60},
  URN =		{urn:nbn:de:0030-drops-253473},
  doi =		{10.4230/LIPIcs.ITCS.2026.60},
  annote =	{Keywords: TFNP, lossy code, randomized proof systems, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.66
A Parameterized-Complexity Framework for Finding Local Optima

Authors: Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz

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

Abstract
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm problem, introduced by Johnson, Papadimitriou, and Yannakakis (1988) fail to capture the methodology of local search algorithms: PLS is concerned with finding a local optimum and not with using local search, while the standard algorithm problem restricts each improvement step to follow a fixed pivoting rule. In this work, we introduce a novel formulation of local search which provides a middle ground between these models. In particular, the task is to output not only a local optimum but also a chain of local improvements leading to it. With this framework, we aim to capture the challenge in designing a good pivoting rule. Especially, when combined with the parameterized complexity paradigm, it enables both strong lower bounds and meaningful tractability results. Unlike previous works that combined parameterized complexity with local search, our framework targets the whole task of finding a local optimum and not only a single improvement step. Focusing on two representative meta-problems - Subset Weight Optimization Problem with the c-swap neighborhood and Weighted Circuit with the flip neighborhood - we establish fixed-parameter tractability results related to the number of distinct weights, while ruling out an analogous result when parameterizing by the distance to the nearest optimum via a new type of reduction.
Cite as

Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz. A Parameterized-Complexity Framework for Finding Local Optima. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 66:1-66:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ganian_et_al:LIPIcs.ITCS.2026.66,
  author =	{Ganian, Robert and Hoang, Hung P. and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Parameterized-Complexity Framework for Finding Local Optima}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{66:1--66:20},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-253532},
  doi =		{10.4230/LIPIcs.ITCS.2026.66},
  annote =	{Keywords: Local Search, Parameterized Complexity, PLS}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.69
Computing Equilibrium Points of Electrostatic Potentials

Authors: Abheek Ghosh, Paul W. Goldberg, and Alexandros Hollender

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

Abstract
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which solutions are guaranteed to exist due to a nonconstructive argument, but gradient descent is unreliable due to the presence of singularities. We present an algorithm based on piecewise approximation of the potential function by Taylor series. The main insight is to divide the domain into a grid with variable coarseness, where grid cells are exponentially smaller in regions where the function changes rapidly compared to regions where it changes slowly. Our algorithm finds approximate equilibrium points in time poly-logarithmic in the approximation parameter, but these points are not guaranteed to be close to exact solutions. Nevertheless, we show that such points can be computed efficiently under a mild assumption that we call "strong non-degeneracy". We complement these algorithmic results by studying a generalization of this problem and showing that it is CLS-hard and in PPAD, leaving its precise classification as an intriguing open problem.
Cite as

Abheek Ghosh, Paul W. Goldberg, and Alexandros Hollender. Computing Equilibrium Points of Electrostatic Potentials. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 69:1-69:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ghosh_et_al:LIPIcs.ITCS.2026.69,
  author =	{Ghosh, Abheek and Goldberg, Paul W. and Hollender, Alexandros},
  title =	{{Computing Equilibrium Points of Electrostatic Potentials}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{69:1--69:22},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-253566},
  doi =		{10.4230/LIPIcs.ITCS.2026.69},
  annote =	{Keywords: Total search problems, TFNP, PPAD, CLS, polynomial equations}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.8
Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds

Authors: Yaroslav Alekseev and Nikita Gaevoy

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

Abstract
Recently, Göös et al. [Göös et al., 2024] showed that Res ⋏ uSA = RevRes in the following sense: if a formula φ has refutations of size at most s and width/degree at most w in both Res and uSA, then there is a refutation for φ of size at most poly(s ⋅ 2^w) in RevRes. Their proof relies on the TFNP characterization of the aforementioned proof systems. In our work, we give a direct and simplified proof of this result, simultaneously achieving better bounds: we show that if for a formula φ there are refutations of size at most s in both Res and uSA, then there is a refutation of φ of size at most poly(s) in RevRes. This potentially allows us to "lift" size lower bounds from RevRes to Res for the formulas for which there are upper bounds in uSA. This kind of lifting was not possible before because of the exponential blow-up in size from the width. Similarly, we improve the bounds in another intersection theorem from [Göös et al., 2024] by giving a direct proof of Res ⋏ uNS = RevResT. Finally, we generalize those intersection theorems to some proof systems for which we currently do not have a TFNP characterization. For example, we show that Res(⊕) ⋏ u-wRes(⊕) = RevRes(⊕), which effectively allows us to reduce the problem of proving Pigeonhole Principle lower bounds in Res(⊕) to proving Pigeonhole Principle lower bounds in RevRes(⊕), a potentially weaker proof system.
Cite as

Yaroslav Alekseev and Nikita Gaevoy. Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{alekseev_et_al:LIPIcs.ITCS.2026.8,
  author =	{Alekseev, Yaroslav and Gaevoy, Nikita},
  title =	{{Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{8:1--8:18},
  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.2026.8},
  URN =		{urn:nbn:de:0030-drops-252953},
  doi =		{10.4230/LIPIcs.ITCS.2026.8},
  annote =	{Keywords: proof complexity, intersection theorems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.7
An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem

Authors: Marco Aldi, Sevag Gharibian, and Dorian Rudolph

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

Abstract
The theory of Total Function NP (TFNP) and its subclasses says that, even if one is promised an efficiently verifiable proof exists for a problem, finding this proof can be intractable. Despite the success of the theory at showing intractability of problems such as computing Brouwer fixed points and Nash equilibria, subclasses of TFNP remain arguably few and far between. In this work, we define two new subclasses of TFNP borne of the study of complex polynomial systems: Multi-homogeneous Systems (MHS) and Sparse Fundamental Theorem of Algebra (SFTA). The first of these is based on Bézout’s theorem from algebraic geometry, marking the first TFNP subclass based on an algebraic geometric principle. At the heart of our study is the computational problem known as Quantum SAT (QSAT) with a System of Distinct Representatives (SDR), first studied by [Laumann, Läuchli, Moessner, Scardicchio, and Sondhi 2010]. Among other results, we show that QSAT with SDR is MHS-complete, thus giving not only the first link between quantum complexity theory and TFNP, but also the first TFNP problem whose classical variant (SAT with SDR) is easy but whose quantum variant is hard. We also show how to embed the roots of a sparse, high-degree, univariate polynomial into QSAT with SDR, obtaining that SFTA is contained in a zero-error version of MHS. We conjecture this construction also works in the low-error setting, which would imply SFTA ⊆ MHS.
Cite as

Marco Aldi, Sevag Gharibian, and Dorian Rudolph. An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{aldi_et_al:LIPIcs.ITCS.2026.7,
  author =	{Aldi, Marco and Gharibian, Sevag and Rudolph, Dorian},
  title =	{{An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{7:1--7:24},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-252946},
  doi =		{10.4230/LIPIcs.ITCS.2026.7},
  annote =	{Keywords: quantum complexity theory, Quantum Merlin Arthur (QMA), Quantum Satisfiability Problem (QSAT), total function NP (TFNP)}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.56
PLS-Completeness of String Permutations

Authors: Dominik Scheder and Johannes Tantow

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

Abstract
Bitstrings can be permuted via permutations and compared via the lexicographic order. In this paper we study the complexity of finding a minimum of a bitstring via given permutations. As finding a global optimum is known to be NP-complete [László Babai and Eugene M. Luks, 1983], we study the local optima via the class PLS [David S. Johnson et al., 1988] and show hardness for PLS. Additionally, we show that even for one permutation the global optimization problem is NP-complete and give a formula that has these permutation as its symmetries. This answers an open question inspired from Kołodziejczyk and Thapen [Leszek Aleksander Kolodziejczyk and Neil Thapen, 2024] and stated at the SAT and interactions seminar in Dagstuhl.
Cite as

Dominik Scheder and Johannes Tantow. PLS-Completeness of String Permutations. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{scheder_et_al:LIPIcs.ESA.2025.56,
  author =	{Scheder, Dominik and Tantow, Johannes},
  title =	{{PLS-Completeness of String Permutations}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{56:1--56:14},
  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.2025.56},
  URN =		{urn:nbn:de:0030-drops-245245},
  doi =		{10.4230/LIPIcs.ESA.2025.56},
  annote =	{Keywords: PLS, total search problems, local search, permutation groups, symmetry}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.95
ARRIVAL: Recursive Framework & 𝓁₁-Contraction

Authors: Sebastian Haslebacher

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

Abstract
ARRIVAL is the problem of deciding which out of two possible destinations will be reached first by a token that moves deterministically along the edges of a directed graph, according to so-called switching rules. It is known to lie in NP ∩ CoNP, but not known to lie in 𝖯. The state-of-the-art algorithm due to Gärtner et al. (ICALP `21) runs in time 2^{𝒪(√n log n)} on an n-vertex graph. We prove that ARRIVAL can be solved in time 2^{𝒪(k log² n)} on n-vertex graphs of treewidth k. Our algorithm is derived by adapting a simple recursive algorithm for a generalization of ARRIVAL called G-ARRIVAL. This simple recursive algorithm acts as a framework from which we can also rederive the subexponential upper bound of Gärtner et al. Our second result is a reduction from G-ARRIVAL to the problem of finding an approximate fixed point of an 𝓁₁-contracting function f : [0, 1]ⁿ → [0, 1]ⁿ. Finding such fixed points is a well-studied problem in the case of the 𝓁₂-metric and the 𝓁_∞-metric, but little is known about the 𝓁₁-case. Both of our results highlight parallels between ARRIVAL and the Simple Stochastic Games (SSG) problem. Concretely, Chatterjee et al. (SODA `23) gave an algorithm for SSG parameterized by treewidth that achieves a similar bound as we do for ARRIVAL, and SSG is known to reduce to 𝓁_∞-contraction.
Cite as

Sebastian Haslebacher. ARRIVAL: Recursive Framework & 𝓁₁-Contraction. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{haslebacher:LIPIcs.ICALP.2025.95,
  author =	{Haslebacher, Sebastian},
  title =	{{ARRIVAL: Recursive Framework \& 𝓁₁-Contraction}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{95:1--95:17},
  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.2025.95},
  URN =		{urn:nbn:de:0030-drops-234723},
  doi =		{10.4230/LIPIcs.ICALP.2025.95},
  annote =	{Keywords: ARRIVAL, G-ARRIVAL, Deterministic Random Walk, Rotor-Routing, 𝓁₁-Contraction, Banach Fixed Point}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.145
Reducing Stochastic Games to Semidefinite Programming

Authors: Manuel Bodirsky, Georg Loho, and Mateusz Skomra

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

Abstract
We present a polynomial-time reduction from max-average constraints to the feasibility problem for semidefinite programs. This shows that Condon’s simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.
Cite as

Manuel Bodirsky, Georg Loho, and Mateusz Skomra. Reducing Stochastic Games to Semidefinite Programming. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 145:1-145:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2025.145,
  author =	{Bodirsky, Manuel and Loho, Georg and Skomra, Mateusz},
  title =	{{Reducing Stochastic Games to Semidefinite Programming}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{145:1--145:15},
  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.2025.145},
  URN =		{urn:nbn:de:0030-drops-235224},
  doi =		{10.4230/LIPIcs.ICALP.2025.145},
  annote =	{Keywords: Mean-payoff games, stochastic games, semidefinite programming, max-average constraints, max-atom problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.71
Unfairly Splitting Separable Necklaces

Authors: Patrick Schnider, Linus Stalder, and Simon Weber

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

Abstract
The Necklace Splitting problem is a classical problem in combinatorics that has been intensively studied both from a combinatorial and a computational point of view. It is well-known that the Necklace Splitting problem reduces to the discrete Ham Sandwich problem. This reduction was crucial in the proof of PPA-completeness of the Ham Sandwich problem. Recently, Borzechowski, Schnider and Weber [ISAAC'23] introduced a variant of Necklace Splitting that similarly reduces to the α-Ham Sandwich problem, which lies in the complexity class UEOPL but is not known to be complete. To make this reduction work, the input necklace is guaranteed to be n-separable. They showed that these necklaces can be fairly split in polynomial time and thus this subproblem cannot be used to prove UEOPL-hardness for α-Ham Sandwich. We consider the more general unfair necklace splitting problem on n-separable necklaces, i.e., the problem of splitting these necklaces such that each thief gets a desired fraction of each type of jewels. This more general problem is the natural necklace-splitting-type version of α-Ham Sandwich, and its complexity status is one of the main open questions posed by Borzechowski, Schnider and Weber. We show that the unfair splitting problem is also polynomial-time solvable, and can thus also not be used to show UEOPL-hardness for α-Ham Sandwich.
Cite as

Patrick Schnider, Linus Stalder, and Simon Weber. Unfairly Splitting Separable Necklaces. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{schnider_et_al:LIPIcs.STACS.2025.71,
  author =	{Schnider, Patrick and Stalder, Linus and Weber, Simon},
  title =	{{Unfairly Splitting Separable Necklaces}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{71:1--71:19},
  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.2025.71},
  URN =		{urn:nbn:de:0030-drops-228963},
  doi =		{10.4230/LIPIcs.STACS.2025.71},
  annote =	{Keywords: Necklace splitting, n-separability, well-separation, Ham Sandwich, alpha-Ham Sandwich, unfair splitting, fair division}
}
  • Refine by Type
  • 23 Document/PDF
  • 16 Document/HTML

  • Refine by Publication Year
  • 11 2026
  • 5 2025
  • 1 2024
  • 2 2021
  • 1 2020
  • Show More...

  • Refine by Author
  • 7 Savani, Rahul
  • 5 Fearnley, John
  • 3 Haslebacher, Sebastian
  • 3 Hoang, Hung P.
  • 3 Schnider, Patrick
  • Show More...

  • Refine by Series/Journal
  • 22 LIPIcs
  • 1 DagRep

  • Refine by Classification
  • 10 Theory of computation → Problems, reductions and completeness
  • 3 Theory of computation → Computational geometry
  • 2 Mathematics of computing → Combinatoric problems
  • 2 Theory of computation → Complexity classes
  • 2 Theory of computation → Continuous optimization
  • Show More...

  • Refine by Keyword
  • 5 TFNP
  • 3 PLS
  • 3 PPAD
  • 2 ARRIVAL
  • 2 CLS
  • 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
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact