Graph Search Problem Research Articles

Single step graph search problem

A variation of the graph search problem is presented. The assumption is that each edge can be searched by any searcher in a single step and the fugitive can move with unbounded speed. The problem is to search a graph in a single step such that no fugitive can hide between the searchers. A sufficient and necessary condition is presented for a graph G = ( V, E) to be single step searchable with ⫫; E⫫ searchers. If ⫫ E⫫ searchers are not enough, it can be shown that to determine the minimum number of extra searchers needed is intractable. An O(⫫ E⫫) algorithm to single step search an interval graph of ⫫ E⫫ edges with the minimum number of extra searchers is also presented.

Design graph search problems with learning: A neural network approach

Design graph search problems with learning: A neural network approach

A frame architecture for a certain class of graph search problems

A frame control strategy is presented which directs an efficient graph search when information available for finding a path is distributed throughout the graph. The frame structure requires (worst case) only O(K/sup N/) memory size instead of O(K/sup 2N/), which is needed for a matrix representation of an N-level, K-branch tree graph. An efficiency analysis is detailed, and its application to a communication system for the nonverbal, severely motor disabled is discussed. >

Efficient Algorithms for Geometric Graph Search Problems

In this paper, we show that many graph search problems can be solved quite efficiently for a geometric intersection graph of horizontal and vertical line segments. We first extract several basic operations for depth first search and breadth first search on a graph. Then we present data structures for the intersection graph in terms of which those operations can be implemented in an efficient manner. The data structures enable us to solve various graph search problems besides depth first search and breadth first search. Specifying the results obtained in this paper for an intersection graph of n horizontal and vertical segments with m pairs of intersecting segments, we obtain algorithms with the following complexity, where $N = \min \{ m,n\log n\} $. (i) Depth first search and breadth first search can be executed in $O(n\log n)$ time and $O(N)$ space. (ii) The biconnected components can be found in $O(n\log n)$ time and $O(N)$ space. (iii) A maximum matching and a maximum independent set can be found in $O...

Parallel algorithms for a depth first search and a breadth first search

Two graph search problems are considered in a parallel computational environment. In this paper, we use the shortest path algorithm as a useful parallel computational technique. Based on the parallel shortest path algorithm presented by Dekel [8], we develop a parallel breadth first search algorithm for general graphs and a parallel depth first search algorithm for acyclic digraphs which run in time O(logd-logn) using 0(n 2[n/log n]) processors. For a breadth first search, the resulting algorithm is the same with that of Ghosh and Bhattacharjee [9]. But the difference between them is that the algorithm presented in [9] is based on the parallel breadth first search algorithm for trees while our algorithm is based on the shortest path algorithm. Furthermore, the algorithms presented in this paper have a unified algorithm structure.

A Search Technique for Clause Interconnectivity Graphs

This paper presents a new representation and technique for proving theorems automatically that is both computationally more effective than resolution and permits a clear and concise formal description. A problem in automatic theorem proving can be specified by a set of clauses, containing literals, that represents a set of axioms and the negation of a theorem to be proved. The set of clauses can be replaced by a graph in which the nodes represent literals and the edges link unifiable complements. The nodes are partitioned by clause membership, and the edges are labeled with a most general unifying substitution. Given this representation, theorem proving becomes a graph-searching problem. The search technique presented here, in effect, unrolls the graph into sets of solution trees. The trees grow in a well-defined breadth-first way that defines a measure of proof complexity.