A frame architecture for a certain class of graph search problems

1988 ◽  
Vol 18 (5) ◽  
pp. 815-824 ◽  
Author(s):  
B.K. Sy ◽  
J.R. Deller
Keyword(s):  
Graph Search ◽  
Search Problems

Efficient Algorithms for Geometric Graph Search Problems

1986 ◽  
Vol 15 (2) ◽  
pp. 478-494 ◽  
Author(s):  
Hiroshi Imai ◽  
Takao Asano
Keyword(s):  
Geometric Graph ◽  
Efficient Algorithms ◽  
Graph Search ◽  
Search Problems

scholarly journals Incremental Symmetry Breaking Constraints for Graph Search Problems

2020 ◽  
Vol 34 (02) ◽  
pp. 1536-1543
Author(s):  
Avraham Itzhakov ◽  
Michael Codish
Keyword(s):  
Problem Solving ◽  
Symmetry Breaking ◽  
Special Property ◽  
Graph Search ◽  
Search Problem ◽  
Search Problems ◽  
Canonical Order ◽  
Parallel Graph ◽  
Canonical Graph

This paper introduces incremental symmetry breaking constraints for graph search problems which are complete and compact. We show that these constraints can be computed incrementally: A symmetry breaking constraint for order n graphs can be extended to one for order n + 1 graphs. Moreover, these constraints induce a special property on their canonical solutions: An order n canonical graph contains a canonical subgraph on the first k vertices for every 1 ≤ k ≤ n. This facilitates a “generate and extend” paradigm for parallel graph search problem solving: To solve a graph search problem φ on order n graphs, first generate the canonical graphs of some order k < n. Then, compute canonical solutions for φ by extending, in parallel, each canonical order k graph together with suitable symmetry breaking constraints. The contribution is that the proposed symmetry breaking constraints enable us to extend the order k canonical graphs to order n canonical solutions. We demonstrate our approach through its application on two hard graph search problems.

scholarly journals A Case of Pathology in Multiobjective Heuristic Search

2013 ◽  
Vol 48 ◽  
pp. 717-732 ◽  
Author(s):  
J.L. Pérez de la Cruz ◽  
L. Mandow ◽  
E. Machuca
Keyword(s):  
Heuristic Search ◽  
Search Algorithm ◽  
Simple Graph ◽  
Graph Search ◽  
Problem Size ◽  
Search Problems ◽  
Heuristic Information ◽  
Blind Search

This article considers the performance of the MOA* multiobjective search algorithm with heuristic information. It is shown that in certain cases blind search can be more efficient than perfectly informed search, in terms of both node and label expansions. A class of simple graph search problems is defined for which the number of nodes grows linearly with problem size and the number of nondominated labels grows quadratically. It is proved that for these problems the number of node expansions performed by blind MOA* grows linearly with problem size, while the number of such expansions performed with a perfectly informed heuristic grows quadratically. It is also proved that the number of label expansions grows quadratically in the blind case and cubically in the informed case.

Best Neighbor Heuristic Search for Finding Minimum Paths in Transportation Networks

1998 ◽  
Vol 1651 (1) ◽  
pp. 48-52 ◽  
Author(s):  
Jeffrey L. Adler
Keyword(s):  
Heuristic Search ◽  
Transportation Networks ◽  
Transportation Network ◽  
Search Problems ◽  
A Algorithm ◽  
Running Time ◽  
Search Effort ◽  
Wide Range ◽  
Path Search ◽  
Sparse Networks

For a wide range of transportation network path search problems, the A* heuristic significantly reduces both search effort and running time when compared to basic label-setting algorithms. The motivation for this research was to determine if additional savings could be attained by further experimenting with refinements to the A* approach. We propose a best neighbor heuristic improvement to the A* algorithm that yields additional benefits by significantly reducing the search effort on sparse networks. The level of reduction in running time improves as the average outdegree of the network decreases and the number of paths sought increases.

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

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