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58th Annual ACM Symposium on Theory of Computing (STOC 2026), June 22–26, 2026,
Salt Lake City, UT, USA
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Article: stoc26foreword-fm003-p
Papers
No Exponential Quantum Speedup for SIS∞ Anymore
Robin Kothari,
Ryan O'Donnell, and
Kewen Wu
(Google Quantum AI, USA; Carnegie Mellon University, USA; Institute for Advanced Study at Princeton, USA)
In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for the average-case ℓ∞-Short Integer Solution (SIS∞) problem, in a parameter range outside the normal range of cryptographic interest, but still with no known efficient classical algorithm. This was particularly exciting since SIS∞ is a simple problem without structure, and their algorithmic techniques were different from those used in prior exponential quantum speedups.
We present efficient classical algorithms for all of the SIS∞ and (more general) Constrained Integer Solution problems studied in their paper, showing there is no exponential quantum speedup anymore.
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Article: stoc26main-p52-p
Incremental Shortest Paths in Almost Linear Time via a Modified Interior Point Method
Yang Liu
(Carnegie Mellon University, USA)
We give an algorithm that takes a directed graph G undergoing m edge insertions with lengths in [1, W], and maintains (1+є)-approximate shortest path distances from a fixed source s to all other vertices. The algorithm is deterministic and runs in total time m1+o(1)logW, for any є > exp(−(logm)0.99). This is achieved by designing a nonstandard interior point method to crudely detect when the distances from s to other vertices v have decreased by a (1+є) factor, and implementing it using the deterministic min-ratio cycle data structure of [Chen-Kyng-Liu-Meierhans-Probst, STOC 2024].
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Article: stoc26main-p55-p
S-Unit Equations in Modules and Linear-Exponential Diophantine Equations
Ruiwen Dong and
Doron Shafrir
(University of Oxford, UK; Ben-Gurion University of the Negev, Israel)
Let T be a positive integer and M be a finitely presented module over the Laurent polynomial ring ℤ/T[X1±, …, XN±]. We consider S-unit equations over M: these are equations of the form x1 m1 + ⋯ + xK mK = m0, where the variables x1, …, xK range over the set of monomials (with coefficient 1) of ℤ/T[X1±, …, XN±]. When T is a power of a prime number p, we show that the solution set of an S-unit equation over M is effectively p-normal in the sense of Derksen and Masser (2015). This generalizes their result on S-unit equations in fields of prime characteristic. When T is an arbitrary positive integer, we show that deciding whether an S-unit equation over M admits a solution is Turing equivalent to solving a system of linear-exponential Diophantine equations, whose base contains the prime divisors of T. Combined with a recent result of Karimov, Luca, Nieuwveld, Ouaknine and Worrell (2025), this yields decidability when T has at most two distinct prime divisors. This also shows that proving either decidability or undecidability in the case of arbitrary T would entail major breakthroughs in number theory. S-unit equations in modules have direct connections to many problems in computational algebra such as finding sparse polynomials in ideals, identifying zeros of linear recurrence sequences, and deciding membership problems in metabelian groups. In particular, a direct consequence of our result is the decidability Submonoid Membership in wreath products of the form ℤ/pa qb ≀ ℤd.
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Article: stoc26main-p56-p
Path Cover, Hamiltonicity, and Independence Number: An FPT Perspective
Fedor V. Fomin,
Petr A. Golovach,
Nikola Jedličková,
Jan Kratochvíl,
Danil Sagunov, and
Kirill Simonov
(University of Bergen, Norway; Charles University, Czech Republic; Saint Petersburg State University, Russian Federation)
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Article: stoc26main-p127-p
An Analytical Approach to Parallel Repetition via CSP Inverse Theorems
Amey Bhangale,
Mark Braverman,
Subhash Khot,
Yang Liu,
Dor Minzer, and
Kunal Mittal
(University of California at Riverside, USA; Princeton University, USA; New York University, USA; Carnegie Mellon University, USA; Massachusetts Institute of Technology, USA)
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Article: stoc26main-p148-p
The Skolem Problem in Rings of Positive Characteristic
Ruiwen Dong and
Doron Shafrir
(University of Oxford, UK; Ben-Gurion University of the Negev, Israel)
We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given a finite presentation of a (unitary) commutative ring R = ℤ/T[X1, …, Xn]/I of characteristic T > 0, and a linear recurrence sequence (γn)n ∈ ℕ ∈ Rℕ, determines whether (γn)n ∈ ℕ contains a zero term. Our proof is based on two recent results: Dong and Shafrir (2026) on the solution set of S-unit equations over pe-torsion modules, and Karimov, Luca, Nieuwveld, Ouaknine, and Worrell (2025) on solving linear equations over powers of two multiplicatively independent numbers. Our result implies, moreover, that the zero set of a linear recurrence sequence over a ring of characteristic T = p1e1 ⋯ pkek is effectively a finite union of pi-normal sets in the sense of Derksen (2007).
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Article: stoc26main-p169-p
Fine-Grained Complexity of Continuous Euclidean k-Center
Lotte Blank,
Karl Bringmann,
Parinya Chalermsook,
Karthik C. S.,
Benedikt Kolbe,
Hung Le, and
Geert van Wordragen
(University of Bonn, Germany; Saarland University, Germany; MPI-INF, Germany; University of Sheffield, UK; Rutgers University, USA; University of Massachusetts at Amherst, USA; Aalto University, Finland)
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Article: stoc26main-p171-p
Sparsifying Suprema of Gaussian Processes
Anindya De,
Shivam Nadimpalli,
Ryan O'Donnell, and
Rocco A. Servedio
(University of Pennsylvania, USA; Massachusetts Institute of Technology, USA; Carnegie Mellon University, USA; Columbia University, USA)
We give a dimension-independent sparsification result for suprema of centered Gaussian processes: Let T be any (possibly infinite) bounded set of vectors in n, and let {t := t · g }t∈ T be the canonical Gaussian process on T, where g∼ N(0, In). We show that there is an Oε(1)-size subset S ⊆ T and a set of real values {cs}s ∈ S such that the random variable sups ∈ S {Xs + cs} is an ε-approximator (in L1) of the random variable supt ∈ T Xt. Notably, the size of the sparsifier S is completely independent of both |T| and the ambient dimension n.
We give two applications of this sparsification theorem: <ul> <li><strong>A “Junta Theorem” for Norms:</strong> We show that given any norm ν(x) on n, there is another norm ψ(x) depending only on the projection of x onto Oε(1) directions, for which ψ(g) is a multiplicative (1 ± ε)-approximation of ν(g) with probability 1−ε for g ∼ N(0,In). </li> <li><strong>Sparsification of Convex Sets:</strong> We show that any intersection of (possibly infinitely many) halfspaces in n that are at distance r from the origin is ε-close (under N(0,In)) to an intersection of only Or,ε(1) halfspaces. This yields new polynomial-time agnostic learning and tolerant property testing algorithms for intersections of halfspaces. </li> </ul>
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Article: stoc26main-p202-p
Determination of the Fifth Busy Beaver Value
The bbchallenge Collaboration,
Justin Blanchard,
Daniel Briggs,
Konrad Deka,
Nathan Fenner,
Yannick Forster,
Georgi Georgiev (Skelet),
Rachel Hunter,
Matthew L. House,
Iijil,
Maja Kądziołka,
Pavel Kropitz,
Shawn Ligocki,
mxdys,
Mateusz Naściszewski,
savask,
Tristan Stérin,
Chris Xu,
Jason Yuen, and
Théo Zimmermann
(bbchallenge.org, USA; None, USA; Inria Paris, France; Sofia University, Bulgaria; University of Warsaw, Poland; PRGM DEV, USA; University of California at San Diego, USA; LTCI - Télécom Paris - Institut Polytechnique de Paris, France)
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Article: stoc26main-p268-p
Perfect Network Resilience in Polynomial Time
Matthias Bentert and
Stefan Schmid
(TU Berlin, Germany; Fraunhofer SIT, Germany)
Modern communication networks support local fast rerouting mechanisms to quickly react to link failures: nodes store a set of conditional rerouting rules which define how to forward an incoming packet in case of incident link failures. Ideally, such rerouting mechanisms provide perfect resilience: any packet is routed from its source s to its target t as long as s and t are still connected in the underlying graph after the link failures. However, ensuring perfect resilience is algorithmically challenging as the rerouting decisions at any node v must rely solely on the local information available at v: the link from which a packet arrived at v (known as the in-port), the target of the packet, and the incident link failures at v. Already in their seminal paper at ACM PODC’12, Feigenbaum, Godfrey, Panda, Schapira, Shenker, and Singla showed that there are instances in which perfect resilience cannot be achieved. While the design of local rerouting algorithms has received much attention since then, we still lack a detailed understanding of when perfect resilience is achievable.
This paper closes this gap and presents a complete characterization of when perfect resilience can be achieved. This characterization also allows us to design an O(n)-time algorithm to decide whether a given instance is perfectly resilient and an O(nm)-time algorithm to compute perfectly resilient rerouting rules whenever it is. Our algorithm is also attractive for the simple structure of the rerouting rules it uses, known as skipping in the literature: alternative links are chosen according to an ordered priority list (per in-port), where failed links are simply skipped. This is also naturally supported in hardware. The size of such an encoding is in Θ(nm) and therefore the running time of our algorithm is optimal when considering skipping rerouting rules. Intriguingly, our result also implies that in the context of perfect resilience, skipping rerouting rules are as powerful as more general rerouting rules that define the out-port for each set of incident failed links explicitly. This partially answers a long-standing open question by Chiesa, Nikolaevskiy, Mitrovic, Gurtov, Madry, Schapira, and Shenker [IEEE/ACM Transactions on Networking, 2017] in the affirmative.
While our algorithm is simple, its analysis is intricate. A key concept in the analysis are links whose two endpoints also form a node separator. We prove that removing those links does not change whether a given instance is perfectly resilient or not. We also show that once all such links are removed, any instance either contains one of four specific rooted minors or belongs to one of three classes. If one of the four rooted minors is contained, then we are dealing with a no-instance (this was previously known for only two of them). Lastly, we show that any instance in any of the three remaining classes is a yes-instance, completing the characterization of perfectly resilient graphs. We do this by showing that simply following a particular face of a planar embedding of the reduced instance using the right-hand rule until a link directly to the target is found is sufficient.
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Article: stoc26main-p277-p
Reviving Thorup’s Shortcut Conjecture
Aaron Bernstein,
Henry Fleischmann,
Maximilian Probst Gutenberg,
Bernhard Haeupler,
Gary Hoppenworth,
Yonggang Jiang,
George Z. Li,
Seth Pettie,
Thatchaphol Saranurak, and
Leon Schiller
(New York University, USA; Carnegie Mellon University, USA; ETH Zurich, Switzerland; INSAIT at Sofia University St. Kliment Ohridski, Bulgaria; University of Michigan, USA; MPI-INF, Germany; Saarland University, Germany; Hasso Plattner Institute - University of Potsdam, Germany)
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Article: stoc26main-p292-p
A Meta-complexity Characterization of Minimal Quantum Cryptography
Bruno Cavalar,
Boyang Chen,
Andrea Coladangelo,
Matthew Gray,
Zihan Hu,
Zhengfeng Ji, and
Xingjian Li
(University of Oxford, UK; Tsinghua University, China; University of Washington, USA; EPFL, Switzerland)
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Article: stoc26main-p298-p
Sample Complexity of Agnostic Multiclass Classification: Natarajan Dimension Strikes Back
Alon Cohen,
Liad Erez,
Steve Hanneke,
Tomer Koren,
Yishay Mansour,
Shay Moran, and
Qian Zhang
(Tel Aviv University, Israel; Google Research, Israel; Purdue University, USA; Technion, Israel)
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Article: stoc26main-p308-p
Oracle Subset Problems: A Meta-algorithm for FPT Approximation via Random Walks
Ishan Chakraborty,
Tanmay Inamdar,
Ariel Kulik,
Madhumita Kundu, and
Saket Saurabh
(Institute of Mathematical Sciences, Chennai, India; IIT Jodhpur, India; Ben-Gurion University of the Negev, Israel; University of Bergen, Norway; Institute of Mathematical Sciences, India)
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Article: stoc26main-p443-p
Memory Reallocation with Polylogarithmic Overhead
Ce Jin
(University of California at Berkeley, USA)
The Memory Reallocation problem asks to dynamically maintain an assignment of given objects of various sizes to non-overlapping contiguous chunks of memory, while supporting updates (insertions/deletions) in an online fashion. The total size of live objects at any time is guaranteed to be at most a 1−є fraction of the total memory. To handle an online update, the allocator may rearrange the objects in memory to make space, and the overhead for this update is defined as the total size of moved objects divided by the size of the object being inserted/deleted.
Our main result is an allocator with worst-case expected overhead polylog(є−1). This exponentially improves the previous worst-case expected overhead O(є−1/2) achieved by Farach-Colton, Kuszmaul, Sheffield, and Westover (2024), narrowing the gap towards the Ω(logє−1) lower bound. Our improvement is based on an application of the sunflower lemma previously used by Erdős and Sárk'ozy (1992) in the context of subset sums.
Our allocator achieves polylogarithmic overhead only in expectation, and sometimes performs expensive rebuilds. Our second technical result shows that this is necessary: it is impossible to achieve subpolynomial overhead with high probability.
Preprint
Article: stoc26main-p510-p
Parallel Sampling via Autospeculation
Nima Anari,
Carlo Baronio,
CJ Chen,
Alireza Haqi,
Frederic Koehler,
Anqi Li, and
Thuy-Duong Vuong
(Stanford University, USA; University of Arizona, USA; University of Chicago, USA; University of California at San Diego, USA)
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Article: stoc26main-p524-p
What Can Be Computed Locally Revisited: First-Order Logic on Sparse Graphs in Distributed Computing
Lelia Blin,
Fedor V. Fomin,
Pierre Fraigniaud,
Sylvain Gay,
Petr A. Golovach,
Pedro Montealegre,
Ivan Rapaport, and
Ioan Todinca
(Université Paris Cité - IRIF - CNRS, France; University of Bergen, Norway; CNRS - Université de Paris, France; École Normale Supérieure, France; Universidad Adolfo Ibáñez, Chile; Universidad de Chile, Chile; Université d'Orléans, France)
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Article: stoc26main-p673-p
Classifying Identities: Subcubic Distributivity Checking and Hardness from Arithmetic Progression Detection
Bartłomiej Dudek,
Nick Fischer,
Geri Gokaj,
Ce Jin,
Marvin Künnemann,
Xiao Mao, and
Mirza Redžić
(University of Wrocław, Poland; MPI-INF, Germany; KIT, Germany; University of California at Berkeley, USA; Stanford University, USA)
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Article: stoc26main-p715-p
Planar Length-Constrained Minimum Spanning Trees
D. Ellis Hershkowitz and
Richard Z. Huang
(Brown University, USA)
In length-constrained minimum spanning tree (MST) we are given an n-node graph G = (V,E) with edge weights w : E → ℤ≥ 0 and edge lengths l: E → ℤ≥ 0 along with a root node r ∈ V and a length constraint h ∈ ℤ≥ 0. Our goal is to output a spanning tree of minimum weight according to w in which every node is at distance at most h from r according to l.
We give a polynomial-time algorithm for planar graphs which, for any constant є > 0, outputs an O(log1+є n)-approximate solution with every node at distance at most (1+є)h from r. Our algorithm is based on new length-constrained versions of classic planar separators and divisions which may be of independent interest. Additionally, our algorithm works for length-constrained Steiner tree and bounds the integrality gap of the natural linear program as O(log2 n /є), again with (1+є) slack in the length constraint. Complementing this, we show that any algorithm on general graphs for length-constrained MST in which nodes are at most 2h from r cannot achieve an approximation of O(log2−є n) for any constant є > 0 under standard complexity assumptions; as such, our results separate the approximability of length-constrained MST in planar and general graphs.
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Article: stoc26main-p778-p
An Optimal Algorithm for Stochastic Vertex Cover
Jan van den Brand,
Inge Li Gørtz,
Chirag Pabbaraju,
Debmalya Panigrahi,
Cliff Stein,
Miltiadis Stouras,
Ola Svensson, and
Ali Vakilian
(Georgia Institute of Technology, USA; DTU, Denmark; Stanford University, USA; Duke University, USA; Columbia University, USA; EPFL, Switzerland; Virginia Tech, USA)
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Article: stoc26main-p798-p
Learning Read-Once Determinants and the Principal Minor Assignment Problem
Abhiram Aravind,
Abhranil Chatterjee,
Sumanta Ghosh,
Rohit Gurjar,
Roshan Raj, and
Chandan Saha
(IISc Bangalore, India; IIT Kanpur, India; ISI Kolkata, India; IIT Bombay, India; Tata Institute of Fundamental Research, Mumbai, India)
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Article: stoc26main-p909-p
Rigorous Implications of the Low-Degree Heuristic
Jun-Ting Hsieh,
Daniel M. Kane,
Pravesh K. Kothari,
Jerry Li,
Sidhanth Mohanty, and
Stefan Tiegel
(Massachusetts Institute of Technology, USA; University of California at San Diego, USA; Princeton University, USA; University of Washington, USA; Northwestern University, USA)
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Article: stoc26main-p995-p
A (4+ϵ)-Approximation for Euclidean 𝑘-Means via Non-monotone Dual-Fitting
Moses Charikar,
Vincent Cohen-Addad,
Ruiquan Gao,
Fabrizio Grandoni,
Euiwoong Lee, and
Ernest van Wijland
(Stanford University, USA; Google Research, France; IDSIA at USI-SUPSI, Switzerland; University of Michigan, USA; Université Paris-Cité - CNRS, France)
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Article: stoc26main-p1152-p
Combinatorial Optimization using Comparison Oracles
Vincent Cohen-Addad,
Tommaso d'Orsi,
Anupam Gupta,
Guru Guruganesh,
Euiwoong Lee,
Renato Paes Leme,
Debmalya Panigrahi,
Madhusudhan Pittu,
Jon Schneider, and
David P. Woodruff
(Google Research, New-York, USA; Bocconi University, Italy; New York University, USA; Google Research, USA; University of Michigan, USA; Duke University, USA; Carnegie Mellon University, USA)
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Article: stoc26main-p1341-p
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