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- research-articleJuly 2024
- research-articleJune 2024
- research-articleJune 2023
Extractors for Images of Varieties
STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of ComputingJune 2023, Pages 46–59https://doi.org/10.1145/3564246.3585109We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map f : Fqr → Fqn to an element sampled uniformly at random from a k-dimensional variety V ⊆ Fqr. ...
- research-articleSeptember 2021
Variety evasive subspace families
CCC '21: Proceedings of the 36th Computational Complexity ConferenceJuly 2021, Article No.: lipics, Page 1https://doi.org/10.4230/LIPIcs.CCC.2021.20We introduce the problem of constructing explicit variety evasive subspace families. Given a family F of sub varieties of a projective or affine space, a collection H of projective or affine k-subspaces is (F, ϵ)-evasive if for every V ∈ F, all but at ...
- research-articleJune 2021
Efficient list-decoding with constant alphabet and list sizes
STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of ComputingJune 2021, Pages 1502–1515https://doi.org/10.1145/3406325.3451046We present an explicit and efficient algebraic construction of capacity-achieving list decodable codes with both constant alphabet and constant list sizes. More specifically, for any R ∈ (0,1) and є>0, we give an algebraic construction of an infinite ...
- research-articleJanuary 2020
Deterministic polynomial factoring over finite fields: A uniform approach via P-schemes
Journal of Symbolic Computation (JOSC), Volume 96, Issue CJan 2020, Pages 22–61https://doi.org/10.1016/j.jsc.2019.02.011AbstractWe introduce a family of combinatorial objects called P -schemes, where P is a collection of subgroups of a finite group G. A P-scheme is a collection of partitions of right coset spaces H \ G, indexed by H ∈ P, that ...
- research-articleJune 2018
Algebraic dependencies and PSPACE algorithms in approximative complexity
CCC '18: Proceedings of the 33rd Computational Complexity ConferenceJune 2018, Article No.: 10, Pages 1–21Testing whether a set f of polynomials has an algebraic dependence is a basic problem with several applications. The polynomials are given as algebraic circuits. Algebraic independence testing question is wide open over finite fields (Dvir, Gabizon, ...
- research-articleJanuary 2015
Gossip vs. Markov chains, and randomness-efficient rumor spreading
SODA '15: Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithmsJanuary 2015, Pages 411–430We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network, and every node is only allowed to call one neighbor in each round. In this work we introduce two fundamentally new ...
- articleJune 2011
Minimum Manhattan Network is NP-Complete
Discrete & Computational Geometry (DCOG), Volume 45, Issue 4June 2011, Pages 701–722Given a set T of n points in ź2, a Manhattan network on T is a graph G with the property that for each pair of points in T, G contains a rectilinear path between them of length equal to their distance in the L1-metric. The minimum Manhattan network ...
- research-articleJune 2009
Minimum Manhattan network is NP-complete
SCG '09: Proceedings of the twenty-fifth annual symposium on Computational geometryJune 2009, Pages 393–402https://doi.org/10.1145/1542362.1542429A rectilinear path between two points p,q∈ R2 is a path connecting p and q with all its line segments horizontal or vertical segments. Furthermore, a Manhattan path between p and q is a rectilinear path with its length exactly dist(p,q):=|p.x-q.x|+|p.y-...
- ArticleDecember 2008
Greedy Construction of 2-Approximation Minimum Manhattan Network
ISAAC '08: Proceedings of the 19th International Symposium on Algorithms and ComputationDecember 2008, Pages 4–15https://doi.org/10.1007/978-3-540-92182-0_4Given a set T of n points in ℝ2, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p,q ε T, in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. ...
- ArticleJune 2008
A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem
AAIM '08: Proceedings of the 4th international conference on Algorithmic Aspects in Information and ManagementJune 2008, Pages 212–223https://doi.org/10.1007/978-3-540-68880-8_21Given a set T of n points in 2, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p , q T , in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance ...