Rounds in communication complexity revisited
SIAM Journal on Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Polygon-containment and translational min-Hausdorff-distance between segment sets are 3SUM-hard
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A fully dynamic algorithm for maintaining the transitive closure
Journal of Computer and System Sciences - STOC 1999
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Preprocessing chains for fast dihedral rotations is hard or even impossible
Computational Geometry: Theory and Applications
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower bounds for linear degeneracy testing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier
Journal of the ACM (JACM)
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Lower bounds for predecessor searching in the cell probe model
Journal of Computer and System Sciences
Subquadratic Algorithms for 3SUM
Algorithmica
Dynamic Connectivity: Connecting to Networks and Geometry
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
ACM SIGACT News
Lower bounds for number-in-hand multiparty communication complexity, made easy
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A little advice can be very helpful
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The cell probe complexity of dynamic range counting
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Mihai Pǎtraşcu: obituary and open problems
ACM SIGACT News
Exact weight subgraphs and the k-sum conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
| Hi-index | 0.00 |
We consider a number of dynamic problems with no known poly-logarithmic upper bounds, and show that they require nΩ(1) time per operation, unless 3SUM has strongly subquadratic algorithms. Our result is modular: (1) We describe a carefully-chosen dynamic version of set disjointness (the "multiphase problem"), and conjecture that it requires n^Omega(1) time per operation. All our lower bounds follow by easy reduction. (2) We reduce 3SUM to the multiphase problem. Ours is the first nonalgebraic reduction from 3SUM, and allows 3SUM-hardness results for combinatorial problems. For instance, it implies hardness of reporting all triangles in a graph. (3) It is plausible that an unconditional lower bound for the multiphase problem can be established via a number-on-forehead communication game.