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Faster Dual-Tree Traversal for Nearest Neighbor Search [chapter]

Ryan R. Curtin
2015 Lecture Notes in Computer Science  
Applied to nearest neighbor search using both kd-trees and ball trees, the new strategy demonstrably outperforms the previous fastest approaches.  ...  When nearest neighbors are desired for a query set instead of a single query point, dual-tree algorithms often provide the fastest solution, especially in low-to-medium dimensions (i.e. up to a hundred  ...  recursion priority is ignored); the standard depth-first prioritized recursion (Algorithm 1); and our improved recursion (Algorithm 4).  ... 
doi:10.1007/978-3-319-25087-8_7 fatcat:vt6o45qvifanpj4umou3wherfq

Forthcoming Papers

2001 Artificial Intelligence  
Recursive conditioning is therefore the first algorithm for exact inference in Bayesian networks to offer a smooth tradeoff between time and space, and to explicate a smooth, quantitative relationship  ...  Darwiche, Recursive conditioning We introduce an any-space algorithm for exact inference in Bayesian networks, called recursive conditioning.  ...  Iterative state-space reduction can be combined with a state-space search, such as best-first search or depth-first branch-and-bound (DFBnB).  ... 
doi:10.1016/s0004-3702(00)00086-2 fatcat:ydglr4s7x5f23fh2vmgoph2mb4

A Simple Framework for the Generalized Nearest Neighbor Problem [chapter]

Tomas Hruz, Marcel Schöngens
2012 Lecture Notes in Computer Science  
We propose a generic method that solves the problem for various classes of query objects and distance functions in a unified way.  ...  The problem of finding a nearest neighbor from a set of points in R d to a complex query object has attracted considerable attention due to various applications in computational geometry, bio-informatics  ...  As stated above, the last recursive call at recursion depth k is handled specially: The set P k is searched point-by-point for a nearest neighbor of Q. Theorem 1.  ... 
doi:10.1007/978-3-642-31155-0_8 fatcat:ejknzg4z7jcc3ekeimlu6g24te

Finding strongly connected components in parallel usingo(log2n) reachability queries

Warren J. Schudy
2008 Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures - SPAA '08  
The runtime is dominated by O(log 2 n) multi-source parallel reachability queries; i.e.  ...  Using Ullman and Yannakakis's [23] techniques for the reachability subroutine gives our algorithm runtimeÕ(t) using mn/t 2 processors for any (n 2 /m) 1/3 ≤ t ≤ n.  ...  Both strongly connected components and topological sort can be computed in linear time using depth-first-search [22] .  ... 
doi:10.1145/1378533.1378560 dblp:conf/spaa/Schudy08 fatcat:r4q6t4hbmjbqdjmd7vtdysurjq

Parallel AND/OR Search for Marginal MAP

Radu Marinescu, Akihiro Kishimoto, Adi Botea
Existing state-of-the-art algorithms for solving exactly this task are based on either depth-first or best-first sequential search over an AND/OR search space.  ...  We also extend the proposed algorithms into depth-first parallel search schemes.  ...  Recursive Best-First AND/OR Search (RBFAOO) (Marinescu, Dechter, and Ihler 2015) extends Recursive Best-First Search (RBFS) (Korf 1993) to MMAP queries and uses a threshold controlling mechanism to  ... 
doi:10.1609/aaai.v34i06.6584 fatcat:zxsgu73lpvggbck4gt45p43g5y

Stabbing Planes [article]

Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere
2022 arXiv   pre-print
Since the middle slab contains no integer points it can be safely discarded, and the algorithm proceeds recursively on the other two branches.  ...  Finally, we prove linear lower bounds on the rank of Stabbing Planes refutations by adapting lower bounds in communication complexity and use these bounds in order to show that Stabbing Planes proofs cannot  ...  We will first present a general procedure for solving the CNF search problem and then show how to instantiate it in both models of communication. Fix an SP refutation of Az ≥ b.  ... 
arXiv:1710.03219v2 fatcat:4dedtl7iordyvcmquixcpwmd6y

Fast Parallel Hypertree Decompositions in Logarithmic Recursion Depth [article]

Georg Gottlob, Matthias Lanzinger, Cem Okulmus, Reinhard Pichler
2021 arXiv   pre-print
However, using HDs for query execution relies on the difficult task of computing decompositions of the query structure, which guides the efficient execution of the query.  ...  The proposed algorithm log-k-decomp requires only a logarithmic number of recursion levels and additionally allows for highly parallelised pruning of the search space by restriction to balanced separators  ...  Thus, using the HD to solve the query gives us guaranteed quadratic upper bounds for the time and space used to answer the query.  ... 
arXiv:2104.13793v1 fatcat:x3tclrkuuzb5plobwkzzs22rs4

Nearest-Neighbor Search on a Time Budget via Max-Margin Trees [chapter]

Parikshit Ram, Dongryeol Lee, Alexander G. Gray
2012 Proceedings of the 2012 SIAM International Conference on Data Mining  
Yet, it still remains difficult to achieve fast query times for state-of-the-art approaches which use multidimensional trees for either exact or approximate search, possibly in combination with hashing  ...  Moreover, a number of these applications only have a limited amount of time to answer nearest-neighbor queries.  ...  Even though tree-based algorithms appear to not scale well to high dimensions, the depth-first search is still conjectured to be a useful strategy [17] -depth-first search on different data structures  ... 
doi:10.1137/1.9781611972825.87 dblp:conf/sdm/RamLG12 fatcat:t2dxw24hn5h2vpuvxricd6lk4u

Solving #SAT and Bayesian Inference with Backtracking Search

F. Bacchus, S. Dalmao, T. Pitassi
2009 The Journal of Artificial Intelligence Research  
In this paper we show that standard backtracking search when augmented with a simple memoization scheme (caching) can solve any sum-of-products problem with time complexity that is at least as good any  ...  Furthermore, backtracking's ability to utilize more flexible variable orderings allows us to prove that it can achieve an exponential speedup over other standard algorithms for SUMPROD on some instances  ...  in DT using a depth-first ordering of the query variables in S(n ao ).  ... 
doi:10.1613/jair.2648 fatcat:bdzl262qsffwtkfn5z44nhhjre

Recursive Query Facilities in Relational Databases: A Survey [chapter]

Piotr Przymus, Aleksandra Boniewicz, Marta Burzańska, Krzysztof Stencel
2010 Communications in Computer and Information Science  
A newer standard, called the SQL-99, introduced recursive queries which can be used to solve such tasks.  ...  The relational model is the basis for most modern databases, while SQL is the most commonly used query language.  ...  For example in order to specify the search order one may use the SEARCH clause with DEPTH FIRST or BREADTH FIRST keywords. The CYCLE clause may be used to detect cycles that could result in loops.  ... 
doi:10.1007/978-3-642-17622-7_10 fatcat:pwmtluvx55echk2zctvy5ukm24

A performance comparison of distance-based query algorithms using R-trees in spatial databases

2007 Information Sciences  
search algorithms (Best-First Search (BFS) and Depth-First Branch-and-Bound (DFBnB)), in terms of disk accesses, response time and main memory requirements, taking into account several important parameters  ...  In this paper, we propose new pruning mechanism to apply them in the design of new Recursive Best-First Search (RBFS) algorithms for DBQs between spatial objects indexed in R-trees.  ...  Here, we review the most representative search algorithms that are widely used for problem solving, they are Best-First Search (BFS), Depth-First Branch-and Bound (DFBnB) and Recursive Best-First Search  ... 
doi:10.1016/j.ins.2006.12.012 fatcat:qwsm3rlmgjgnlb7qq37oxos26e

Controlling recursive inference

David E. Smith, Michael R. Genesereth, Matthew L. Ginsberg
1986 Artificial Intelligence  
In general, the control of recursive inference involves demonstrating that recursive portions of a search space will not contribute any new answers to the problem beyond a certain level.  ...  Here we show how knowledge of the properties of the relations involved and knowledge about the contents of the system's database can be used to prove that portions of a search space will not contribute  ...  Jeff Finger, Pat Hayes, and Richard Waldinger provided useful pointers to related work on program verification and Richard Treitel and Jeff Ullman provided pointers to related work on databases and logic  ... 
doi:10.1016/0004-3702(86)90003-2 fatcat:etyxpuofbfftndrr777nzxglku

Fractal Approximate Nearest Neighbour Search in Log-Log Time

Martin Stommel, Stefan Edelkamp, Thiemo Wiedemeyer, Michael Beetz
2013 Procedings of the British Machine Vision Conference 2013  
The Hilbert curve has already been used to optimise high-dimensional nearest neighbour queries in the context of data base systems.  ...  We show that our algorithms solve two particular nearest neighbor problems efficiently.  ...  The neighbours of a query point q can then be found by using the successor function of the queue. A Hilbert curve of recursive depth R subdivides the unit square into 2 R rows and columns.  ... 
doi:10.5244/c.27.18 dblp:conf/bmvc/StommelEWB13 fatcat:irat2w33ynddrifyfy452i3wpm

Using Expert Knowledge in Database-Oriented Problem Solving

Jiawei Han, Larry Travis
1985 International Conference on Information Systems  
Database-ori ented problem solving often involves the processing of deduction rules which may be recursive in relational database systems.  ...  merged into relational database systems and the compilation to answer queries and solve problems.  ...  planner RELPLAN, then discusses the compilation of presents us algorithms which compile queries involving non-recursive and recursive queries using expen knowlrecursive rules into iterative programs.  ... 
dblp:conf/icis/HanT85 fatcat:ossmsnv2qzgqdddtj4fq4ccruq

A Hierarchical Voxel Hash for Fast 3D Nearest Neighbor Lookup [chapter]

Bertram Drost, Slobodan Ilic
2013 Lecture Notes in Computer Science  
In addition, voxels are stored in a hash table and a bisection on the voxel level is used to find the leaf voxel containing the query point.  ...  The method uses a hierarchical voxel approximation of the data point's Voronoi cells.  ...  To avoid infinite recursion, a limit L max on the depth of the octree is enforced.  ... 
doi:10.1007/978-3-642-40602-7_33 fatcat:xrw2s45vonbibamd36nv63pm5u
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