Richard B. Borie

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This paper describes a predicate calculus in which graph problems can be expressed. Any problem possessing such an expression can be solved in linear time on any recursively constructed graph, once its decomposition tree is known. Moreover, the linear-time algorithm can be generatedautomatically from the expression, because all our theorems are proved(More)
We study pursuit-evasion problems where a number of pursuers have to clear a given graph. We study when polynomial-time algorithms exist to determine howmany pursuers are needed to clear a given graph and how a given number of pursuers should move on the graph to clear it with either a minimum sum of their travel distances or minimum task-completion time.(More)
Recent work in the design of efficient algorithms for optimization problems on treedecomposable graphs concentrates on developing general approaches which lead to families of related algorithms, rather than on developing isolatedad hoc algorithms. This paper develops new general approaches to obtain two new families of related polynomial-time algorithms for(More)
The popular class of series-parallel graphs can be built recursively from single edges by combining smaller components via connections only at a fixed pair of vertices called terminals. This recursive construction property with a limited number ofterminals is essential to the linear time solution ofproblems on these graphs. A second useful property of these(More)
Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed. This article first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive graph classes. Specific classes include trees,(More)
We study the classical edge-searching pursuit-evasion problem where a number of pursuers have to clear a given graph of fast-moving evaders despite poor visibility, for example, where robots search a cave system to ensure that no terrorists are hiding in it. We study when polynomial-time algorithms exist to determine how many robots are needed to clear a(More)