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Subcubic Equivalences Between Path, Matrix, and Triangle Problems
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/net.3230120406openalex-snapshot
An efficient algorithm for K shortest simple paths
inferredcites →https://doi.org/10.1006/jcss.1997.1388openalex-snapshot
On the Exponent of the All Pairs Shortest Path Problem
inferredcites →https://doi.org/10.1007/11523468_21openalex-snapshot
Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs
inferredcites →https://doi.org/10.1007/11534273_28openalex-snapshot
All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time
inferredcites →https://doi.org/10.1007/11786986_24openalex-snapshot
Finding the Smallest H-Subgraph in Real Weighted Graphs and Related Problems
inferredcites →https://doi.org/10.1007/3-540-60922-9_46openalex-snapshot
Universal hashing and k-wise independent random variables via integer arithmetic without primes
inferredcites →https://doi.org/10.1007/978-3-540-30140-0_52openalex-snapshot
On Dynamic Shortest Paths Problems
inferredcites →https://doi.org/10.1007/978-3-642-04128-0_37openalex-snapshot
A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication
inferredcites →https://doi.org/10.1007/978-3-642-31594-7_44openalex-snapshot
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
inferredcites →https://doi.org/10.1007/978-3-662-47672-7_89openalex-snapshot
An Improved Combinatorial Algorithm for Boolean Matrix Multiplication
inferredcites →https://doi.org/10.1007/bf02165411openalex-snapshot
Gaussian elimination is not optimal
inferredcites →https://doi.org/10.1007/pl00009478openalex-snapshot
Geometric Applications of a Randomized Optimization Technique
inferredcites →https://doi.org/10.1007/s00453-007-9036-3openalex-snapshot
Subquadratic Algorithms for 3SUM
inferredcites →https://doi.org/10.1007/s00453-010-9441-xopenalex-snapshot
A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication
inferredcites →https://doi.org/10.1007/s004930050052openalex-snapshot
Quick Approximation to Matrices and Applications
inferredcites →https://doi.org/10.1016/0020-0190(71)90006-8openalex-snapshot
Efficient determination of the transitive closure of a directed graph
inferredcites →https://doi.org/10.1016/0020-0190(76)90085-5openalex-snapshot
An algorithm for finding all shortest paths using N2.81 infinite-precision multiplications
inferredcites →https://doi.org/10.1016/0020-0190(91)90071-oopenalex-snapshot
Computing dominances in En
inferredcites →https://doi.org/10.1016/0925-7721(95)00022-2openalex-snapshot
On a class of O(n2) problems in computational geometry
inferredcites →https://doi.org/10.1016/j.comgeo.2011.11.006openalex-snapshot
On a class of O(n2) problems in computational geometry
inferredcites →https://doi.org/10.1016/j.dam.2007.03.023openalex-snapshot
Open problems around exact algorithms
inferredcites →https://doi.org/10.1016/s0022-0000(75)80046-8openalex-snapshot
General context-free recognition in less than cubic time
inferredcites →https://doi.org/10.1016/s0076-5392(09)x6008-xopenalex-snapshot
Fuzzy Sets and Systems - Theory and Applications
inferredcites →https://doi.org/10.1016/s0747-7171(08)80013-2openalex-snapshot
Matrix multiplication via arithmetic progressions
inferredcites →https://doi.org/10.1017/cbo9780511581274openalex-snapshot
Concentration of Measure for the Analysis of Randomized Algorithms
inferredcites →https://doi.org/10.1017/s0308210511001648openalex-snapshot
Improved bound for complexity of matrix multiplication
inferredcites →https://doi.org/10.1109/focs.2009.76openalex-snapshot
Regularity Lemmas and Combinatorial Algorithms
inferredcites →https://doi.org/10.1109/sfcs.1978.34openalex-snapshot
Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations
inferredcites →https://doi.org/10.1109/sffcs.1999.814635openalex-snapshot
All pairs shortest paths in undirected graphs with integer weights
inferredcites →https://doi.org/10.1109/swat.1971.4openalex-snapshot
Boolean matrix multiplication and transitive closure
inferredcites →https://doi.org/10.1137/0209027openalex-snapshot
New Fast Algorithms for Matrix Operations
inferredcites →https://doi.org/10.1137/0222071openalex-snapshot
Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths
inferredcites →https://doi.org/10.1137/070695149openalex-snapshot
Finding a Heaviest Vertex-Weighted Triangle Is not Harder than Matrix Multiplication
inferredcites →https://doi.org/10.1137/08071990xopenalex-snapshot
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
inferredcites →https://doi.org/10.1137/080730950openalex-snapshot
On the k Shortest Simple Paths Problem in Weighted Directed Graphs
inferredcites →https://doi.org/10.1137/1.9780898715859openalex-snapshot
Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
inferredcites →https://doi.org/10.1137/1.9781611977912openalex-snapshot
Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
inferredcites →https://doi.org/10.1137/s0097539704441629openalex-snapshot
Approximating the Cut-Norm via Grothendieck's Inequality
inferredcites →https://doi.org/10.1137/s0097539795290477openalex-snapshot
Finding the k Shortest Paths
inferredcites →https://doi.org/10.1145/1132516.1132550openalex-snapshot
Finding a maximum weight triangle in n 3-Δ time, with applications
inferredcites →https://doi.org/10.1145/1186810.1186815openalex-snapshot
On the difficulty of some shortest path problems
inferredcites →https://doi.org/10.1145/1236457.1236460openalex-snapshot
Dynamic ordered sets with exponential search trees
inferredcites →https://doi.org/10.1145/1250790.1250876openalex-snapshot
All-pairs bottleneck paths for general graphs in truly sub-cubic time
inferredcites →https://doi.org/10.1145/1250790.1250877openalex-snapshot
More algorithms for all-pairs shortest paths in weighted graphs
inferredcites →https://doi.org/10.1145/1798596.1798597openalex-snapshot
Finding heaviest H -subgraphs in real weighted graphs, with applications
inferredcites →https://doi.org/10.1145/1806689.1806772openalex-snapshot
Towards polynomial lower bounds for dynamic problems
inferredcites →https://doi.org/10.1145/1824777.1824790openalex-snapshot
Nondecreasing paths in a weighted graph or
inferredcites →https://doi.org/10.1145/200836.200880openalex-snapshot
Designing programs that check their work
inferredcites →https://doi.org/10.1145/2213977.2214056openalex-snapshot
Multiplying matrices faster than coppersmith-winograd
inferredcites →https://doi.org/10.1145/2344422.2344423openalex-snapshot
Replacement paths and k simple shortest paths in unweighted directed graphs
inferredcites →https://doi.org/10.1145/2591796.2591811openalex-snapshot
Faster all-pairs shortest paths via circuit complexity
inferredcites →https://doi.org/10.1145/2608628.2608664openalex-snapshot
Powers of tensors and fast matrix multiplication
inferredcites →https://doi.org/10.1145/28869.28874openalex-snapshot
Fibonacci heaps and their uses in improved network optimization algorithms
inferredcites →https://doi.org/10.1145/505241.505242openalex-snapshot
Fast context-free grammar parsing requires fast boolean matrix multiplication
inferredcites →https://doi.org/10.1145/567112.567114openalex-snapshot
All pairs shortest paths using bridging sets and rectangular matrix multiplication
inferredcites →https://doi.org/10.1287/mnsc.17.11.712openalex-snapshot
Finding the K Shortest Loopless Paths in a Network
inferredcites →https://doi.org/10.1287/mnsc.18.7.401openalex-snapshot
A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem
inferredcites →https://doi.org/10.4036/iis.2000.99openalex-snapshot
Algorithms for the Maximum Subarray Problem Based on Matrix Multiplication.
inferredcites →https://doi.org/10.5555/1070432.1070591openalex-snapshot
Quantum algorithms for the triangle problem
inferredcites →https://doi.org/10.5555/1283383.1283482openalex-snapshot
On the K-simple shortest paths problem in weighted directed graphs
inferredcites →https://doi.org/10.5555/1283383.1283490openalex-snapshot
Matrix-vector multiplication in sub-quadratic time: (some preprocessing required)
inferredcites →https://doi.org/10.5555/1496770.1496813openalex-snapshot
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths
inferredcites →https://doi.org/10.5555/1873601.1873662openalex-snapshot
A nearly optimal algorithm for approximating replacement paths and k shortest simple paths in general graphs
inferredcites →https://doi.org/10.5555/2095116.2095232openalex-snapshot
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
inferredcites →https://doi.org/10.5555/2616915.2616941openalex-snapshot
A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication
inferredcites →https://doi.org/10.82444/warw.33495880openalex-snapshot
Finding a heaviest triangle is not harder than matrix multiplication
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Finding Small Complete Subgraphs Efficiently
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Gomory Group Minimization Problem and Its Applications
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Verifying the Product of Generalized Boolean Matrix Multiplication and Its Applications to Detect Small Subgraphs
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Computing Replacement Paths in the CONGEST Model
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A Time-Efficient Output-Sensitive Quantum Algorithm for Boolean Matrix Multiplication
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Parameterized Aspects of Triangle Enumeration
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Lower Bounds for Tropical Circuits and Dynamic Programs
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Maximum Matching in Almost Linear Time on Graphs of Bounded Clique-Width
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Improved Merlin–Arthur Protocols for Central Problems in Fine-Grained Complexity
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Applications of random algebraic constructions to hardness of approximation
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K-shortest simple paths using biobjective path search
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Sampling and sparsification for approximating the packedness of trajectories and detecting gatherings
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An Efficient Seed-Initialized Algorithm for Maximal Clique Enumeration and Its Applications
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Algorithms and Conditional Lower Bounds for Planning Problems
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Detecting and enumerating small induced subgraphs in c -closed graphs
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Efficient parameterized algorithms for computing all-pairs shortest paths
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Shortest distances as enumeration problem
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Finding the largest triangle in a graph in expected quadratic time
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Tight bounds for reachability problems on one-counter and pushdown systems
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Improved bounds for rectangular monotone Min-Plus Product and applications
inferred← citeshttps://doi.org/10.1016/j.ipl.2024.106555openalex-snapshot
New bounds for the number of lightest cycles in undirected graphs
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Parameterized aspects of triangle enumeration
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Pushing the Online Boolean Matrix-vector Multiplication conjecture off-line and identifying its easy cases
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Bisection of bounded treewidth graphs by convolutions
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Consequences of APSP, triangle detection, and 3SUM hardness for separation between determinism and non-determinism
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Finding and counting small tournaments in large tournaments
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Finer-grained reductions in fine-grained hardness of approximation
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k-shortest simple paths in bounded treewidth graphs
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Two algorithms for shortest-paths problems in edge-weighted directed graphs
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Finding influential cores via normalized Ricci flows in directed and undirected hypergraphs with applications
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Minimum Weight Cycles and Triangles: Equivalences and Algorithms
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Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization
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Improved Quantum Algorithm for Triangle Finding via Combinatorial Arguments
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Sensitive Distance and Reachability Oracles for Large Batch Updates
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New Techniques for Proving Fine-Grained Average-Case Hardness
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Monochromatic Triangles, Triangle Listing and APSP
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Applications of Random Algebraic Constructions to Hardness of Approximation
inferred← citeshttps://doi.org/10.1109/focs52979.2021.00112openalex-snapshot
APMF < APSP? Gomory-Hu Tree for Unweighted Graphs in Almost-Quadratic Time
inferred← citeshttps://doi.org/10.1109/focs54457.2022.00035openalex-snapshot
Fitting Metrics and Ultrametrics with Minimum Disagreements
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Induced Cycles and Paths Are Harder Than You Think
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Breaking the Cubic Barrier for All-Pairs Max-Flow: Gomory-Hu Tree in Nearly Quadratic Time
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Faster Approximation Algorithms for Computing Shortest Cycles on Weighted Graphs
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New hardness results for planar graph problems in p and an algorithm for sparsest cut
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Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (Unless APSP Can)
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Multiple Source Replacement Path Problem
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Subcubic algorithms for Gomory–Hu tree in unweighted graphs
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Hardness for triangle problems under even more believable hypotheses: reductions from real APSP, real 3SUM, and OV
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Output-sensitive Conjunctive Query Evaluation
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Simple Closure Analysis Revisited
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Any-k evaluation of conjunctive queries and its application to graph pattern matching
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k-shortest path: average-case analysis and practical improvements
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On the Maximum Triangle Problem
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Fast Algorithms for Energy Games in Special Cases
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Triangles and Girth in Disk Graphs and Transmission Graphs
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On the Fine-Grained Complexity of Parity Problems
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Near Optimal Algorithm for the Directed Single Source Replacement Paths Problem
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Fully Dynamic Algorithms for Minimum Weight Cycle and Related Problems
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Counting 4-Patterns in Permutations Is Equivalent to Counting 4-Cycles in Graphs
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Fine-Grained Complexity of Regular Path Queries
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Parameterized Fine-Grained Reductions
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MapReduce Meets Fine-Grained Complexity: MapReduce Algorithms for APSP, Matrix Multiplication, 3-SUM, and Beyond
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Truly Subcubic Min-Plus Product for Less Structured Matrices, with Applications
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Multiple Metric Learning for Structured Data
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New Hardness Results for Planar Graph Problems in P and an Algorithm for Sparsest Cut
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Conditional Lower Bound for Inclusion-Based Points-to Analysis
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Hardness of Approximate Nearest Neighbor Search under L-infinity
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A systematic association of subgraph counts over a network
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Approximation Algorithms for Min-Distance Problems in DAGs
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Does Preprocessing help in Fast Sequence Comparisons?
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Decremental All-Pairs Shortest Paths in Deterministic Near-Linear Time
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