scholarly journals Searching Monotone Arrays: A Survey

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 10
Author(s):  
Márcia R. Cappelle ◽  
Les R. Foulds ◽  
Humberto J. Longo
Keyword(s):  
Finite Dimension ◽  
Search Algorithms ◽  
Search Problem ◽  
Open Problems ◽  
Worst Case ◽  
Real Value

Given a monotone ordered multi-dimensional real array A and a real value k, an important question in computation is to establish if k is a member of A by sequentially searching A by comparing k with some of its entries. This search problem and its known results are surveyed, including the case when A has sizes not necessarily equal. Worst case search algorithms for various types of arrays of finite dimension and sizes are reported. Each algorithm has order strictly less than the product of the sizes of the array. Present challenges and open problems in the area are also presented.

TWO-DIMENSIONAL RANGE SEARCH BASED ON THE VORONOI DIAGRAM

2005 ◽  
Vol 15 (02) ◽  
pp. 151-166
Author(s):  
TAKESHI KANDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Voronoi Diagram ◽  
Dimensional Space ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Average Case ◽  
Range Search ◽  
Almost All ◽  
Set Of Points ◽  
Dimensional Range

This paper studies the two-dimensional range search problem, and constructs a simple and efficient algorithm based on the Voronoi diagram. In this problem, a set of points and a query range are given, and we want to enumerate all the points which are inside the query range as quickly as possible. In most of the previous researches on this problem, the shape of the query range is restricted to particular ones such as circles, rectangles and triangles, and the improvement on the worst-case performance has been pursued. On the other hand, the algorithm proposed in this paper is designed for a general shape of the query range in the two-dimensional space, and is intended to accomplish a good average-case performance. This performance is actually observed by numerical experiments. In these experiments, we compare the execution time of the proposed algorithm with those of other representative algorithms such as those based on the bucketing technique and the k-d tree. We can observe that our algorithm shows the better performance in almost all the cases.

On the functional complexity of a two-dimensional interval search problem

2002 ◽  
Vol 12 (1) ◽  
Author(s):  
E.E. Gasanov ◽  
I.V. Kuznetsova
Keyword(s):  
Search Time ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Logarithmic Average ◽  
Functional Complexity

AbstractWe suggest a modification of the Bentley-Maurer algorithm which solves a twodimensional interval search problem. This modification allows us to decrease the initially logarithmic average search time to constant, retaining the logarithmic worst-case search time. This algorithm depends on a parameter whose change results in variation of the needed memory from Ϭ(k

scholarly journals Intruder capture algorithms considering visible intruders

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984673
Author(s):  
Jonghoek Kim
Keyword(s):  
Real Time ◽  
Weighted Graph ◽  
Search Algorithms ◽  
Tree Graph ◽  
Multiple Robots ◽  
Weighted Tree ◽  
Topological Map ◽  
Worst Case ◽  
Minimum Number ◽  
Full Knowledge

In this article, we consider the problem of using multiple robots (searchers) to capture intruders in an environment. Assume that a robot can access the position of an intruder in real time, that is, an intruder is visible by a robot. We simplify the environment so that robots and worst-case intruders move along a weighted graph, which is a topological map of the environment. In such settings, a worst-case intruder is characterized by unbounded speed, complete awareness of searcher location and intent, and full knowledge of the search environment. The weight of an edge or a vertex in a weighted graph is a cost describing the clearing requirement of the edge or the vertex. This article provides non-monotone search algorithms to capture every visible intruder. Our algorithms are easy to implement, thus are suitable for practical robot applications. Based on the non-monotone search algorithms, we derive the minimum number of robots required to clear a weighted tree graph. Considering a general weighted graph, we derive bounds for the number of robots required. Finally, we present switching algorithms to improve the time efficiency of capturing intruders while not increasing the number of robots. We verify the effectiveness of our approach using MATLAB simulations.

scholarly journals Worst-case & average-case Efficiency trade-offs for search problems

2021 ◽  
Author(s):  
Preeti Sharma
Keyword(s):  
Search Problem ◽  
Worst Case ◽  
Evacuation Time ◽  
Average Case ◽  
Deterministic Algorithms ◽  
Trade Offs ◽  
Time Work ◽  
Research Problems ◽  
Work Done ◽  
Vast Area

Evacuation problems fall under the vast area of search theory and operations research. Problems of evacuation of two robots on a unit disc have been studied for an efficient evacuation time. Work done so far has focused on improving the ’worst-case’ evacuation time with deterministic algorithms. We study the ’average-case’ evacuation time (randomized algorithms) while considering the efficiency trade-off between worst-case and average-case costs. Our other contribution is to analyze average-case and worst-case costs for the cowpath problem (another search problem) which helped us to set a parallel method for the evacuation problem.

scholarly journals Enriching Non-Parametric Bidirectional Search Algorithms

2019 ◽  
Vol 33 ◽  
pp. 2379-2386
Author(s):  
Shahaf S. Shperberg ◽  
Ariel Felner ◽  
Nathan R. Sturtevant ◽  
Solomon E. Shimony ◽  
Avi Hayoun
Keyword(s):  
Search Algorithm ◽  
Search Algorithms ◽  
Optimal Solutions ◽  
Worst Case ◽  
Bidirectional Search ◽  
Algorithmic Framework ◽  
Special Case ◽  
Non Parametric

NBS is a non-parametric bidirectional search algorithm proven to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

Complexity Research on B Algorithm

2010 ◽  
Vol 20-23 ◽  
pp. 173-177
Author(s):  
Ai Li Han
Keyword(s):  
Time Complexity ◽  
Complexity Analysis ◽  
Search Algorithms ◽  
Heuristic Function ◽  
Worst Case ◽  
Intelligent Search ◽  
The Cost

The time complexity of B algorithm, one of the intelligent search algorithms, is discussed. By anatomizing some instances, it is pointed out that the cost of calculating the value of heuristic function should be included in the range of time complexity analysis for B algorithm. And then, an algorithm of calculating the value of heuristic function is presented. By analyzing the cost of calculating the value of heuristic function, it is pointed out that the number of recursions in B algorithm is O(n!) in the worst case. Therefore, the time complexity of B algorithm is exponential instead of O(n2).

Methods for Parallelizing Constraint Propagation through the Use of Strong Local Consistencies

2018 ◽  
Vol 27 (04) ◽  
pp. 1860002 ◽  
Author(s):  
Minas Dasygenis ◽  
Kostas Stergiou
Keyword(s):  
Search Space ◽  
Constraint Propagation ◽  
Search Tree ◽  
Search Algorithms ◽  
Combinatorial Problems ◽  
Search Process ◽  
Worst Case ◽  
Arc Consistency ◽  
Local Propagation ◽  
Propagation Methods

Constraint programming (CP) is a powerful paradigm for various types of hard combinatorial problems. Constraint propagation techniques, such as arc consistency (AC), are used within solvers to prune inconsistent values from the domains of the variables and narrow down the search space. Local consistencies stronger than AC have the potential to prune the search space even more, but they are not widely used because they incur a high run time penalty in cases where they are unsuccessful. All constraint propagation techniques are sequential by nature, and thus they cannot be scaled up to modern multicore machines. For this reason, research on parallelizing constraint propagation is very limited. Contributing towards this direction, we exploit the parallelization possibilities of modern CPUs in tandem with strong local propagation methods in a novel way. Instead of trying to parallelize constraint propagation algorithms, we propose two search algorithms that apply different propagation methods in parallel. Both algorithms consist of a master search process, which is a typical CP solver, and a number of slave processes, with each one implementing a strong propagation method. The first algorithm runs the different propagators synchronously at each node of the search tree explored in the master process, while the second one can run them asynchronously at different nodes of the search tree. Preliminary experimental results on well-established benchmarks display the promise of our research by illustrating that our algorithms have execution times equal to those of serial solvers, in the worst case, while being faster in most cases.

scholarly journals FORMULATION OF A FAMILY OF SURE-SUCCESS QUANTUM SEARCH ALGORITHMS

2004 ◽  
Vol 02 (03) ◽  
pp. 285-293
Author(s):  
JIN-YUAN HSIEH ◽  
CHE-MING LI ◽  
JENN-SEN LIN ◽  
DER-SAN CHUU
Keyword(s):  
Quantum Algorithms ◽  
Search Algorithms ◽  
Search Problem ◽  
Quantum Search ◽  
Matching Conditions ◽  
Quantum Search Algorithms ◽  
Grover Search ◽  
Phase Angles

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding formulae for evaluating the iterations or oracle calls required in the search computation. We also present how to adjust the phase angles in the generalized Grover operator to ensure the sure-success if minimal oracle calls are demanded in the search.

Lower bounds of temporal and spatial complexity of the substring search problem

2014 ◽  
Vol 24 (6) ◽  
Author(s):  
Evgeniy M. Perper
Keyword(s):  
Lower Bounds ◽  
Search Algorithms ◽  
Search Problem ◽  
Spatial Complexity ◽  
Running Time ◽  
Temporal And Spatial

AbstractWe consider the problem of substring search in a set of strings. The problem is the following: given a set of strings and an arbitrary substring, list all strings from the set that contain this substring.We describe search algorithms and obtain lower bounds for the running time and for the memory volume required by the fastest algorithms

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