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.

Tidal Flow: A Fast and Teachable Maximum Flow Algorithm

2018 ◽  
Vol 12 ◽  
pp. 25-41
Author(s):  
Matthew C. FONTAINE
Keyword(s):  
Computer Science ◽  
Tidal Flow ◽  
Maximum Flow ◽  
Efficient Algorithms ◽  
Science Students ◽  
Flow Algorithm ◽  
Maximum Flows

Among the most interesting problems in competitive programming involve maximum flows. However, efficient algorithms for solving these problems are often difficult for students to understand at an intuitive level. One reason for this difficulty may be a lack of suitable metaphors relating these algorithms to concepts that the students already understand. This paper introduces a novel maximum flow algorithm, Tidal Flow, that is designed to be intuitive to undergraduate andpre-university computer science students.

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