Which Problems Have Strongly Exponential Complexity?
2001/12/01 by Russell Impagliazzo, Ramamohan Paturi, Francis Zane · 1,364 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics #Complexity and Algorithms in Graphs #Complexity class #Discrete mathematics #Exponential function #Machine Learning and Algorithms #Mathematics #Time complexity #Upper and lower bounds
paper · doi:10.1006/jcss.2001.1774
published in Journal of Computer and System Sciences 63(4), 512-530 (Elsevier BV)
openalex publication_date 2001/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
Cited by
- Revenue maximization in Stackelberg Pricing Games: beyond the combinatorial setting
- PCP Theorems, SETH and More: Towards Proving Sub-linear Time Inapproximability
- The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise
- Towards Tight Approximation Bounds for Graph Diameter and Eccentricities
- On the Complexity Landscape of Connected f -Factor Problems
- Knapsack Problems: A Parameterized Point of View
- On the Fine-grained Complexity of One-Dimensional Dynamic Programming
- Polynomial Kernels for Weighted Problems
- Lossy Kernelization
- CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial Representations
- Why walking the dog takes time: Frechet distance has no strongly subquadratic algorithms unless SETH fails
- Inapproximability of Maximum Biclique Problems, Minimum k-Cut and Densest At-Least-k-Subgraph from the Small Set Expansion Hypothesis
- Hardness of Approximate Nearest Neighbor Search under L-infinity
- A Proof Checking View of Parameterized Complexity
- On Fine-Grained Exact Computation in Regular Graphs
- Detecting communities is hard, and counting them is even harder
- On the Computational Complexity of MapReduce
- On Structural Parameterizations of Hitting Set: Hitting Paths in Graphs Using 2-SAT
- Subexponential-time Algorithms for Maximum Independent Set in Pt-free and Broom-free Graphs
- Into the Square - On the Complexity of Quadratic-Time Solvable Problems
- Parameterized Complexity of Bandwidth on Trees
- On the Parameterized Complexity and Kernelization of the Workflow Satisfiability Problem
- Popular conjectures imply strong lower bounds for dynamic problems
- Dynamic Programming for Graphs on Surfaces
- Lower Bounds for QBFs of Bounded Treewidth
- A New Direction for Counting Perfect Matchings
- The Relative Exponential Time Complexity of Approximate Counting Satisfying Assignments
- A randomized polynomial kernelization for Vertex Cover with a smaller parameter
- Subexponential and FPT-time Inapproximability of Independent Set and Related Problems
- Multivariate Complexity Analysis of Geometric \sc Red Blue Set Cover
- Quadratic-Time Hardness of LCS and other Sequence Similarity Measures
- Kernels for (connected) Dominating Set on graphs with Excluded Topological subgraphs
- On the complexity of detecting hazards
- Circuit Depth Reductions
- Half-integrality, LP-branching and FPT Algorithms
- Simultaneous Feedback Vertex Set: A Parameterized Perspective
- Improved Lower Bounds for Graph Embedding Problems
- Parameterized Max Min Feedback Vertex Set
- Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints
- On the Subexponential Time Complexity of CSP
- Treewidth-Aware Complexity in ASP: Not all Positive Cycles are Equally Hard
- Exploiting Treewidth for Projected Model Counting and its Limits
- Enumerating Minimal Connected Dominating Sets
- Inapproximability of VC Dimension and Littlestone's Dimension
- Parameterized complexity dichotomy for (r,ℓ)-Vertex Deletion
- On the dynamic width of the 3-colorability problem
- On the (adjacency) metric dimension of corona and strong product graphs and their local variants: combinatorial and computational results
- Self-reducible with easy decision version counting problems admit additive error approximation. Connections to counting complexity, exponential time complexity, and circuit lower bounds
- Fixing improper colorings of graphs
- What is known about Vertex Cover Kernelization?
- Parameterized Algorithms for Steiner Forest in Bounded Width Graphs
- Sampling-based bottleneck pathfinding with applications to Frechet matching
- Parameterized Complexity of Critical Node Cuts
- Sitting closer to friends than enemies, revisited
- A Polynomial Kernel for Trivially Perfect Editing
- Simpler Partial Derandomization of PPSZ for k-SAT
- On Treewidth and Stable Marriage
- On Sparsification for Computing Treewidth
- Improved approximation algorithm for the Dense-3-Subhypergraph Problem
- On the optimality of approximation schemes for the classical scheduling problem
- The role of planarity in connectivity problems parameterized by treewidth
- Consistent Subset Sampling
- 3SUM, 3XOR, Triangles
- Tight Bounds for Subgraph Isomorphism and Graph Homomorphism
- Subexponential fixed-parameter tractability of cluster editing
- Another Hamiltonian Cycle in Bipartite Pfaffian Graphs
- On Exact Algorithms for Permutation CSP
- On the Equivalence among Problems of Bounded Width
- Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis
- Approximate Clustering with Same-Cluster Queries
- A Casual Tour Around a Circuit Complexity Bound
- Universal Factor Graphs
- Tight Lower Bounds on Graph Embedding Problems
- Polynomial kernelization for removing induced claws and diamonds
- Using a Skewed Hamming Distance to Speed Up Deterministic Local Search
- Complexity of Token Swapping and Its Variants
- Tractable hypergraph properties for constraint satisfaction and conjunctive queries
- Subexponential parameterized algorithms for graphs of polynomial growth
- Almost Optimal Time Lower Bound for Approximating Parameterized Clique, CSP, and More, under ETH
- Computing the Tutte polynomial in vertex-exponential time
- Tractability of Konig Edge Deletion Problems
- Ruling out FPT algorithms for Weighted Coloring on forests
- Determinant Sums for Undirected Hamiltonicity
- A Tight Analysis of Greedy Yields Subexponential Time Approximation for Uniform Decision Tree
- A Duality Between Depth-Three Formulas and Approximation by Depth-Two
- The inverse Voronoi problem in graphs
- Improved integrality gap upper bounds for TSP with distances one and two
- A Fixed-Parameter Algorithm for #SAT with Parameter Incidence Treewidth
- The Long, the Short and the Random
- Towards a more efficient approach for the satisfiability of two-variable logic
- Polynomial kernels collapse the W-hierarchy
- Complexity of counting subgraphs: only the boundedness of the vertex-cover number counts
- Parameterizing the Permanent: Genus, Apices, Minors, Evaluation mod 2k
- Stable Marriage with Covering Constraints: A Complete Computational\n Trichotomy
- Width-parameterized SAT: Time-Space Tradeoffs
- On independence domination
- Johnson Coverage Hypothesis: Inapproximability of k-means and k-median\n in Lp metrics
- Fine-grained Meta-Theorems for Vertex Integrity
- A Note on the Complexity of Computing the Number of Reachable Vertices\n in a Digraph
- Approximating the diameter of a graph
- Algorithms and Complexity Results for Exact Bayesian Structure Learning
- Treewidth and Counting Projected Answer Sets
- Fast Hamiltonicity checking via bases of perfect matchings
- On the Parameterized Complexity of Graph Modification to First-Order Logic Properties
- FO Model Checking on Posets of Bounded Width
- Algorithms and Almost Tight Results for 3-Colorability of Small Diameter Graphs
- Computing the Tutte Polynomial in Vertex-Exponential Time
- Fully Polynomial-Time Parameterized Computations for Graphs and Matrices of Low Treewidth
- Sublinear Maximum Inner Product Search using Concomitants of Extreme Order Statistics
- Coping with the NP-Hardness of the Graph Bandwidth Problem
- Exact Algorithms for Treewidth and Minimum Fill-In
- Complexity of Grundy Coloring and Its Variants
- Tight Hardness Results for LCS and Other Sequence Similarity Measures
- Hardness of Approximation Between P and NP
- Lossy kernelization
- Parameterized Approximation Algorithms for Bidirected Steiner Network Problems
- Fixed-parameter algorithms for DAG Partitioning
- On the Parameterized Complexity of Approximating Dominating Set
- Fixed-Parameter Approximations for k-Center Problems in Low Highway Dimension Graphs
- Diameter Spanners, Eccentricity Spanners, and Approximating Extremal Distances
- Pathwidth of cubic graphs and exact algorithms
- Strong computational lower bounds via parameterized complexity
- Invitation to Fixed-Parameter Algorithms
- Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth
- A Subexponential Parameterized Algorithm for Proper Interval Completion
- On Problems as Hard as CNF-SAT
- A measure & conquer approach for the analysis of exact algorithms
- Improved Parameterized Upper Bounds for Vertex Cover
- Subexponential Parameterized Algorithm for Minimum Fill-In
- Approximating the maximum clique minor and some subgraph homeomorphism problems
- On Directed Feedback Vertex Set Parameterized by Treewidth
- Sparsification and subexponential approximation
- Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament
- Finding Points in General Position
- Subexponential Algorithms for Unique Games and Related Problems
- On Problems Equivalent to (min,+)-Convolution
- Independent Set on Pk-Free Graphs in Quasi-Polynomial Time
- Parameterized Algorithms for Power-Efficiently Connecting Wireless Sensor Networks: Theory and Experiments
- Exponential Time Complexity of the Permanent and the Tutte Polynomial
- Time Complexity of Constraint Satisfaction via Universal Algebra
- Hitting and Harvesting Pumpkins
- Structural Decompositions of Epistemic Logic Programs
- Modern Lower Bound Techniques in Database Theory and Constraint Satisfaction
- A note on hardness of diameter approximation
- The Complexity of Satisfiability of Small Depth Circuits
- On Moderately Exponential Time for SAT
- The Exponential Time Hypothesis and the Parameterized Clique Problem
- Hardness of Equations over Finite Solvable Groups Under the Exponential Time Hypothesis
- Known Algorithms on Graphs of Bounded Treewidth are Probably Optimal
- Known Algorithms for Edge Clique Cover are Probably Optimal
- Improving exhaustive search implies superpolynomial lower bounds
- Domination When the Stars Are Out
- Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
- Exact algorithms for the Hamiltonian cycle problem in planar graphs
- Linear Kernels and Linear-Time Algorithms for Finding Large Cuts
- Clique problem [wikipedia]
- Exponential time hypothesis [wikipedia]
- New enumeration algorithm for protein structure comparison and classification. [europepmc]
- A graph modification approach for finding core-periphery structures in protein interaction networks. [europepmc]
- Sitting Closer to Friends than Enemies, Revisited. [europepmc]
- Separating OR, SUM, and XOR Circuits. [europepmc]
- New Tools and Connections for Exponential-Time Approximation. [europepmc]
- Stable Matchings with Covering Constraints: A Complete Computational Trichotomy. [europepmc]
- Approximating Vector Scheduling: Almost Matching Upper and Lower Bounds. [europepmc]
- Obtaining a Proportional Allocation by Deleting Items. [europepmc]
- Missing value replacement in strings and applications. [europepmc]
- Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. [europepmc]
- On the Fine Grained Complexity of Finite Automata Non-emptiness of Intersection [europepmc]
- A Faster Algorithm for Propositional Model Counting Parameterized by Incidence Treewidth [europepmc]