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Lower bounds for set intersection queries

P. Dietz, K. Mehlhorn, R. Raman, C. Uhrig
1995 Algorithmica  
We have a collection of initially empty sets and would like to process an intermixed sequence of n updates (insertions into and deletions from individual sets) and q queries (reporting the intersection  ...  We consider the following set intersection reporting problem.  ...  If the answers to all the queries were to be obtained by unioning together singleton sets, then the lower bound would follow.  ... 
doi:10.1007/bf01293666 fatcat:qw7yweewojgihdn4amljtlf4xa

Lower Bounds for Semialgebraic Range Searching and Stabbing Problems [article]

Peyman Afshani, Pingan Cheng
2021 arXiv   pre-print
In the semialgebraic range searching problem, we are to preprocess n points in ℝ^d s.t. for any query range from a family of constant complexity semialgebraic sets, all the points intersecting the range  ...  We give the first nontrivial lower bounds for semilagebraic range searching and related problems.  ...  The authors would like to thank Esther Ezra for sparking the initial ideas behind the proof. References  ... 
arXiv:2012.00704v3 fatcat:puqtxc54vvbypdvieb2rpvgmlm

Lower Bounds for Sorted Geometric Queries in the I/O Model [chapter]

Peyman Afshani, Norbert Zeh
2012 Lecture Notes in Computer Science  
This bound is unlikely to be optimal and in fact we can show that, for a particular class of "persistence-based" data structures, the space lower bound can be improved to Ω(N 2 /M O(1) ).  ...  Both these lower bounds are a first step towards understanding the complexity of sorted geometric query problems.  ...  We would like to thank Timothy Chan for bringing the type of problems we study in this paper to our attention.  ... 
doi:10.1007/978-3-642-33090-2_6 fatcat:ojvmxpckh5c27jich47vrupneu

Indexing the Earth Mover's Distance Using Normal Distributions [article]

Brian E. Ruttenberg, Ambuj K. Singh
2011 arXiv   pre-print
It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.  ...  We propose a new lower bound to the EMD that approximates the EMD on a projection vector.  ...  (3) to compute a lower bound to the projected EMD at query time.  ... 
arXiv:1111.7168v1 fatcat:3ei2f6joo5brvn3oxi3dzhwvsm

Indexing the earth mover's distance using normal distributions

Brian E. Ruttenberg, Ambuj K. Singh
2011 Proceedings of the VLDB Endowment  
It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.  ...  We propose a new lower bound to the EMD that approximates the EMD on a projection vector.  ...  (3) to compute a lower bound to the projected EMD at query time.  ... 
doi:10.14778/2078331.2078336 fatcat:d43h6bmz7nablp3qz5q5qeljcu

Two-Dimensional Range Diameter Queries [chapter]

Pooya Davoodi, Michiel Smid, Freek van Walderveen
2012 Lecture Notes in Computer Science  
We provide evidence for the hardness of designing space-efficient data structures that support range diameter queries by giving a reduction from the set intersection problem.  ...  We strengthen the evidence by giving a lower bound for an important subproblem arising in solutions to the range diameter problem: computing the diameter of two convex polygons, that are separated by a  ...  We would like to thank Elad Verbin for introducing the set intersection problem, and Gerth Stølting Brodal, Jakob Truelsen, Konstantinos Tsakalidis, and Qin Zhang for informative discussions.  ... 
doi:10.1007/978-3-642-29344-3_19 fatcat:cib7ffpsrjejnfhn4pdge75scm

Improved range searching lower bounds

Kasper Green Larsen, Huy Le Nguyen
2012 Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12  
We prove our lower bounds by constructing a hard input set and query set, and then invoking Chazelle and Rosenberg's [CGTA'96] general theorem on the complexity of navigation in the pointer machine.  ...  For the group model, we show that input sets and query sets that are hard for range reporting in the pointer machine (i.e. by Chazelle and Rosenberg's theorem), are also hard for dynamic range searching  ...  We also presented the first lower bounds for approximate range reporting in the pointer machine.  ... 
doi:10.1145/2261250.2261275 dblp:conf/compgeom/LarsenN12 fatcat:cth67a7xwnadrc7zpay2ubycry

The Query Complexity of Witness Finding [chapter]

Akinori Kawachi, Benjamin Rossman, Osamu Watanabe
2014 Lecture Notes in Computer Science  
of {0, 1} n and prove an Ω(n 2 ) lower bound for the class of intersection queries (queries of the form "W ∩ S = ∅?"  ...  Our main results are tight lower bounds on m(Q) for a few specific classes of queries (namely, intersection queries, monotone queries and NP queries).  ...  In addition, we considered the setting where witness sets are affine subspaces of {0, 1} n and proved a tight lower bound of Ω(n 2 ) for intersection queries.  ... 
doi:10.1007/978-3-319-06686-8_17 fatcat:pgbbrcawmvdo7bqc27hnokcc5m

Lower bounds for intersection searching and fractional cascading in higher dimension

Bernard Chazelle, Ding Liu
2004 Journal of computer and system sciences (Print)  
Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in Oðk þ polylogðnÞÞ time, using subquadratic storage?  ...  If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time with subcubic storage?  ...  The same lower bound holds for intersecting a query line with a simple polygon with n vertices. 3.  ... 
doi:10.1016/j.jcss.2003.07.003 fatcat:e2fadppxvfbqjjnt2js7yk7bc4

Lower bounds for intersection searching and fractional cascading in higher dimension

Bernard Chazelle, Ding Liu
2001 Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC '01  
Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in Oðk þ polylogðnÞÞ time, using subquadratic storage?  ...  If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time with subcubic storage?  ...  The same lower bound holds for intersecting a query line with a simple polygon with n vertices. 3.  ... 
doi:10.1145/380752.380818 dblp:conf/stoc/ChazelleL01 fatcat:qr6xnf23jzfmdnglqzddx46bpa

The Query Complexity of Witness Finding

Akinori Kawachi, Benjamin Rossman, Osamu Watanabe
2016 Theory of Computing Systems  
of {0, 1} n and prove an Ω(n 2 ) lower bound for the class of intersection queries (queries of the form "W ∩ S = ∅?"  ...  Our main results are tight lower bounds on m(Q) for a few specific classes of queries (namely, intersection queries, monotone queries and NP queries).  ...  In addition, we considered the setting where witness sets are affine subspaces of {0, 1} n and proved a tight lower bound of Ω(n 2 ) for intersection queries.  ... 
doi:10.1007/s00224-016-9708-y fatcat:yufghjgen5a2xi35gcbovnirry

New lower bounds for Hopcroft's problem

J. Erickson
1996 Discrete & Computational Geometry  
We establish new lower bounds on the complexity of the following basic geometric problem, attributed to John Hopcroft: Given a set of n points and m hyperplanes in R d, is any point contained in any hyperplane  ...  We develop our lower bounds in two stages.  ...  New Lower Bounds for Hopcroft's Problem  ... 
doi:10.1007/bf02712875 fatcat:ck34d6ahpzcphibnj7zns72cay

Mihai Pǎtraşcu

Mikkel Thorup
2013 ACM SIGACT News  
In a regular instance, for some set size parameter s ≤ u, each set has size at most s, and each element appears in ns/u sets. query: for given (i, j) ∈ [n] 2 , the boolean query is whether S i intersects  ...  Consider regular set intersection instances with n sets, universe size u, and set size s = log a n.  ... 
doi:10.1145/2447712.2447737 fatcat:rv36df66ufgjfhyhccqhe4ktbe

Data Structure Lower Bounds for Document Indexing Problems [article]

Peyman Afshani, Jesper Sindahl Nielsen
2016 arXiv   pre-print
The problems that we consider are set intersection queries (both the reporting variant and the semi-group counting variant), indexing a set of documents for two-pattern queries, or forbidden- pattern queries  ...  Often our lower bounds match the known space-query time trade-off curve and in fact for all the problems considered, there is a very good and reasonable match between the our lower bounds and the known  ...  We thank Karl Bringmann for simplifying the construction of our documents for the 2P problem. We thank Moshe Lewenstein for bringing the WCI problem to our attention.  ... 
arXiv:1604.06264v1 fatcat:4b56qaqfjfdkxjykcvn73wnery

Box-Trees and R-Trees with Near-Optimal Query Time

Agarwal, de Berg, Gudmundsson, M. Hammar, H. J. Haverkort
2002 Discrete & Computational Geometry  
We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal.  ...  We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points.  ...  We can use this lemma to prove lower bounds for several settings. By substituting µ = (n/t) 1−1/d , we prove the following lower bound for point queries. Theorem 2.3.  ... 
doi:10.1007/s00454-002-2817-1 fatcat:p3noisksmvhxvlt4pssi6vsrkm
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