Complexity
Computational complexity, P vs NP, and lower bounds
20 papers indexed
The complexity of minimum-density locating-dominating set in infinite periodic graphs
The paper proves that finding a minimum-density locating-dominating set in infinite Z-periodic graphs is NP-hard.
Algebraic Circuits Over Sum and Shift and Existential Presburger Arithmetic with Divisibility
This paper proves that the satisfiability problem of existential Presburger arithmetic extended with divisibility predicates (EPAD) is PP-hard.
Trellis State Complexity as an Exact Tropical Factorization Rank
This paper proves that the min-plus factorization rank and tropical rank of a binary linear code's conditional decoding matrix equal 2^s, where s is the classical state complexity of the minimal trell…
Explainable PQC: A Layered Interpretive Framework for Post-Quantum Cryptographic Security Assumptions
The paper proposes 'Explainable PQC,' a layered interpretive framework designed to structure and clarify how post-quantum cryptographic security assumptions are represented and communicated, particula…
Euclidean SVP is deterministically NP-hard to approximate within any constant factor
The Euclidean shortest vector problem is deterministically NP-hard to approximate within any constant factor for arbitrary constants.
Algorithms and complexity for geodetic sets on interval and chordal graphs
This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…
Symmetric Numerical Three-Dimensional Matching: Intractability and Inapproximability
This paper proves the strong NP-completeness and APX-completeness of the Symmetric Numerical Three-Dimensional Matching problem.
On Cutting Cakes and Crossing Curves
The paper shows that the envy-free cake-cutting problem with three agents is intractable and establishes the first lower bounds for the Jordan curve problem.
Scheduling Tasks towards Energy Autarky: Benefits and Computational Costs of Flexibility
This paper studies the autarky problem of scheduling energy-consuming jobs with time windows using a battery and an energy forecast, and shows NP-hardness, polynomial-time solvability, and fixed-param…
The Polynomial-Time Low-Degree Conjecture is False
The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…
Self-Referential $K$-SAT and the Finite Analogue of Gödel's Incompleteness Theorem
Wen Fang, Xianxian Li, Jun Liu, Jie Luo +2 more
This paper establishes a finite combinatorial version of Gödel's incompleteness theorems in Boolean $K$-SAT, resolving assignment correlations and constructing structurally irreducible SAT/UNSAT pairs…
Gap-Majority Lemmas in Communication Complexity
The paper proves an information-theoretically optimal gap-majority lemma in the two-player randomized communication model, achieving the correct linear scaling and constant-constant tradeoff.
Low-degree estimation thresholds in planted hypergraphs and tensor PCA
The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…
Towards Worst-case Hardness for Low-Noise LPN
Divesh Aggarwal, Rishav Gupta, Hai Hoang Nguyen, Kel Zin Tan +1 more
The paper presents a new worst-case to average-case reduction for the Learning Parity with Noise (LPN) problem, achieving hardness for inverse-polynomial noise rates previously unattainable.
On the Complexity of Graph Edit Distance in Restricted Graph Classes
The paper investigates the relationship between graph classes, edit cost functions, and computational complexity of the graph edit distance, providing polynomial-time reductions and correspondences.
XOR Games at Full Tilt: The Hardness of Binary Nonlocal Games
This paper studies a variant of the quantum XOR game model, called tilted XOR games, and shows that approximating their quantum value to constant precision is RE-complete.
Efficient Discrete Position Design for Movable Antenna Systems: Low Complexity and Robustness
Haonan Wang, Xianghao Yu, Rui Wang, Ang Li +1 more
This paper proposes a low-complexity algorithm for maximizing mutual information in a multi-user MIMO uplink communication system using discrete movable antennas.
Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs
Martinsson and Steiner's conjecture on the fractional chromatic number of triangle-free graphs with girth at least 5 is confirmed, and a lower bound is established in a stronger form.
Fundamental Sensing Limits of 6G Cooperative MIMO-ISAC Networks: Joint Position-Velocity CRLB and Decoupling Analysis
This paper derives Cramér-Rao lower bounds for cooperative MIMO integrated sensing and communication networks, considering position and velocity coupling in the Fisher information matrix.
Ulam Median is NP-hard for Four Permutations
The paper shows that finding a median under Ulam distance for four permutations is NP-hard, improving upon previous results.