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.
The smallest programmable machine and the hardness of analyzing it
The paper investigates the computational complexity of deterministic k-pebble automata and their relation to finite automata and Kolmogorov complexity.
Improved Approximation and Hardness Results for the Monitoring Edge-Geodetic Set Problem
The paper presents new approximation and hardness results for the Monitoring Edge-Geodetic Set problem.
The Tournament Equilibrium Set Is PSPACE-Complete, Even under Hereditary Uniqueness
This paper proves that the problem of deciding whether a given alternative belongs to the tournament equilibrium set (TEQ) is PSPACE-complete, and studies the complexity of the problem under different…
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…
Orienting mixed graphs for reachability pairs: When the all pairs setting is easier than the general one
This paper compares the computational complexity of two problems related to orienting mixed graphs to satisfy a maximum number of pairs of vertices.
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…
Approximability limits for bounded-degree max-LINSAT and implications for decoded quantum interferometry
This paper proves that certain optimization problems are NP-hard and provides a complexity-theoretic benchmark for quantum algorithms.
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.
SINR-Aware Base Station Deployment in Wide Area IoT Sensor Networks
The paper proposes a SINR-aware greedy algorithm for base station deployment in IoT sensor networks to achieve near-optimal coverage while reducing computational effort.
Subjective Valuations Make It Hard to be Fair: The Complexity of Resource Allocation to Groups of Agents
This paper studies the parameterized complexity of finding an EF1 allocation of indivisible items in the group-sharing setting.
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…
The Computational Complexity of Team Zero-Sum Games
The paper establishes that computing Nash equilibria in team zero-sum games is PPAD-complete.
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…
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…