P. Dearing - Academia.edu (original) (raw)

Papers by P. Dearing

Primal and dual algorithms are developed for solving the n-dimensional convex optimization proble... more Primal and dual algorithms are developed for solving the n-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers m given Euclidean balls, each with given center and radius. Each algorithm is based on a directional search method in which a search path may be a ray or a two-dimensional conic section in IRn. At each iteration, a search path is constructed by the intersection of bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional hyperboloids. The optimal step size along each search path is determined explicitly.

Code 55 7a NAME OF MONITORING ORGANIZATION 6c. ADDRESS {City, State, and ZIP Code) Monterey, Cali... more Code 55 7a NAME OF MONITORING ORGANIZATION 6c. ADDRESS {City, State, and ZIP Code) Monterey, California 93943-5000 7b ADDRESS (C/ty. State, and ZIP Code) 8a. NAME OF FUNDING-SPONSORING ORGANIZATION 8b OFFICE SYMBOL {If applicable) 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 8c. ADDRESS (Dry, State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERS

Journal of Research of the National Institute of Standards and Technology, 2006

The one-center location problem in the plane, also called the one facility min-max location probl... more The one-center location problem in the plane, also called the one facility min-max location problem, may be stated as follows: given m points p i ∈ IR 2 , i = 1, 2, ..., m, and some distance function d(x, y) for x, y ∈ IR 2 , the problem is to determine the location of a point x ∈ IR 2 that minimizes the maximum distance d(p i , x) over i = 1, ..., m. The problem is denoted by P1 and written as follows: The equivalent, constrained version of P1 is written as follows: P1: min z s.t. z ≥ d(p i , x) i = 1, ..., m. Problem P1 was first reported by Sylvester [6] using Euclidean distance. A substantial number of papers have appeared on the one-center problem assuming a variety of distances. Articles and books with reviews of the literature include Hearn and Vijay, [4], Drezner [1], Drezner and Hamacher [2]. A related problem is the one-median, or total-cost, location problem in which the maximum operator is replaced by the summation operator. Both the center and the median problems have been studied extensively for Euclidean distance, for l p distances for 1 ≤ p ≤ ∞, and on networks [1,2]. Witzgall [9] considered the median problem for polyhedral norms and noted that the problem could be formulated as a linear programming problem. He also noted that "the linear program had special properties that should be exploited for an efficient solution", and that "more research in this area is indicated." Ward and Wendell [8] considered both the one-median and the one-center problems using block distance, which is the special case of polyhedral distances in which the polytope is symmetric. For both the onemedian and the one-center problems they reported two

Operations Research Letters, 1985

Operations Research, 1983

This paper investigates a class of single-facility location problems on an arbitrary network. Nec... more This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.

arXiv: General Mathematics, 2017

Closed form expressions are given for computing the parameters and vectors that identify and defi... more Closed form expressions are given for computing the parameters and vectors that identify and define the n−1n-1n−1 dimensional conic section that results from the intersection of a hyperplane with an nnn-dimensional conic section: cone, hyperboloid of two sheets, ellipsoid or paraboloid. The conic sections are assumed to be symmetric about their major axis, but may have any orientation and center. A class of hyperboloids are identified with the property that the parameters and vectors of the intersection of all hyperboloids in a subset of the class can be computed efficiently.

Discrete Applied Mathematics, 1993

Bibelnieks, E. and P.M. Dearing, Neighborhood subtree tolerance graphs, Discrete Applied Mathemat... more Bibelnieks, E. and P.M. Dearing, Neighborhood subtree tolerance graphs, Discrete Applied Mathematics 43 (1993) 13-26. In this paper, we introduce neighborhood subtree tolerance (NeST) graphs which are defined in terms of the tolerance-intersection of neighborhood subtrees of a tree. This class of graphs extends the class of interval tolerance graphs which are defined in terms of the tolerance-intersection of intervals on the real line. Interval tolerance graphs were first introduced by Golumbic and Monma as tolerance graphs. Some relationships among interval tolerance, NeST, and weakly triangulated graphs are examined. The main result shows that NeST graphs are weakly triangulated graphs. In addition, proper NeST graphs are shown to be exactly bounded NeST graphs and NeST graphs with constant tolerance are shown to be strongly chordal.

Operations Research Letters, 2009

A dual type algorithm constructs the minimum covering ball of a given finite set of points in R n... more A dual type algorithm constructs the minimum covering ball of a given finite set of points in R n by finding the minimum covering balls of a sequence of subsets, each with no more than n + 1 points and with strictly increasing radius, until all points are covered. (P.M. Dearing). center, without violating the covering property, until optimality is reached. Elzinga and Hearn [4] developed a dual approach in which the minimum covering circle is found for a sequence of subsets S ⊆ P, each of at most 3 points and with increasing radius, until some circle covers the entire set P. Other approaches use Voronoi diagrams . Meggido [6] developed a theoretical linear time algorithm for solving the problem.

Transportation Science, 1974

Transportation Science is the foremost journal in the field of transportation analysis, featuring... more Transportation Science is the foremost journal in the field of transportation analysis, featuring comprehensive, timely articles and surveys that cover all levels of planning and all modes of transportation. It is a quarterly journal published by the Institute for Operations Research and ...

Transportation Science, 1992

Operations Research, 1976

ABSTRACT

Operations Research, 1983

This paper investigates a class of single-facility location problems on an arbitrary network. Nec... more This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.

Journal of Global Optimization, 2013

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given... more The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in IR n is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration.

IIE Transactions, 1987

... and Implentation Depanment. bought on the outside market, finished at the Calhoun Mill ... On... more ... and Implentation Depanment. bought on the outside market, finished at the Calhoun Mill ... One approach to the above situation is to develop a linear programming model to maxim~ze profit subject to the re-quirements that demand he met and that loom capacity not be exceeded. ...

Annals of Operations Research, 2005

... They can also be viewed as a generalization of distances in fixed orientations as introduced ... more ... They can also be viewed as a generalization of distances in fixed orientations as introduced inWidmayer, Wu, and Wong (1987) where it is assumed that all ... from an origin point, xo = (xo, yo)T to a destination point xd = (xd, yd)T , denoted P(xo,xd), is a rectifiable, Jordan arc (see ...

Discrete Applied Mathematics, 1988

An algorithm for finding maximal chordal subgraphs is developed that has worst-case time complexi... more An algorithm for finding maximal chordal subgraphs is developed that has worst-case time complexity of O(IE(B), where IEI is the number of edges in G and d is the maximum vertex degree in G. The study of maximal chordal subgraphs is motivated by their usefulness as computationally efficient structures with which to approximate a general graph. Two examples are given that illustrate potential applications of maximal chordal subgraphs. One provides an alternative formulation to the maximum independent set problem on a graph. The other involves a novel splitting scheme for solving large sparse systems of linear equations.

Primal and dual algorithms are developed for solving the n-dimensional convex optimization proble... more Primal and dual algorithms are developed for solving the n-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers m given Euclidean balls, each with given center and radius. Each algorithm is based on a directional search method in which a search path may be a ray or a two-dimensional conic section in IRn. At each iteration, a search path is constructed by the intersection of bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional hyperboloids. The optimal step size along each search path is determined explicitly.

Code 55 7a NAME OF MONITORING ORGANIZATION 6c. ADDRESS {City, State, and ZIP Code) Monterey, Cali... more Code 55 7a NAME OF MONITORING ORGANIZATION 6c. ADDRESS {City, State, and ZIP Code) Monterey, California 93943-5000 7b ADDRESS (C/ty. State, and ZIP Code) 8a. NAME OF FUNDING-SPONSORING ORGANIZATION 8b OFFICE SYMBOL {If applicable) 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 8c. ADDRESS (Dry, State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERS

Journal of Research of the National Institute of Standards and Technology, 2006

The one-center location problem in the plane, also called the one facility min-max location probl... more The one-center location problem in the plane, also called the one facility min-max location problem, may be stated as follows: given m points p i ∈ IR 2 , i = 1, 2, ..., m, and some distance function d(x, y) for x, y ∈ IR 2 , the problem is to determine the location of a point x ∈ IR 2 that minimizes the maximum distance d(p i , x) over i = 1, ..., m. The problem is denoted by P1 and written as follows: The equivalent, constrained version of P1 is written as follows: P1: min z s.t. z ≥ d(p i , x) i = 1, ..., m. Problem P1 was first reported by Sylvester [6] using Euclidean distance. A substantial number of papers have appeared on the one-center problem assuming a variety of distances. Articles and books with reviews of the literature include Hearn and Vijay, [4], Drezner [1], Drezner and Hamacher [2]. A related problem is the one-median, or total-cost, location problem in which the maximum operator is replaced by the summation operator. Both the center and the median problems have been studied extensively for Euclidean distance, for l p distances for 1 ≤ p ≤ ∞, and on networks [1,2]. Witzgall [9] considered the median problem for polyhedral norms and noted that the problem could be formulated as a linear programming problem. He also noted that "the linear program had special properties that should be exploited for an efficient solution", and that "more research in this area is indicated." Ward and Wendell [8] considered both the one-median and the one-center problems using block distance, which is the special case of polyhedral distances in which the polytope is symmetric. For both the onemedian and the one-center problems they reported two

Operations Research Letters, 1985

Operations Research, 1983

This paper investigates a class of single-facility location problems on an arbitrary network. Nec... more This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.

arXiv: General Mathematics, 2017

Closed form expressions are given for computing the parameters and vectors that identify and defi... more Closed form expressions are given for computing the parameters and vectors that identify and define the n−1n-1n−1 dimensional conic section that results from the intersection of a hyperplane with an nnn-dimensional conic section: cone, hyperboloid of two sheets, ellipsoid or paraboloid. The conic sections are assumed to be symmetric about their major axis, but may have any orientation and center. A class of hyperboloids are identified with the property that the parameters and vectors of the intersection of all hyperboloids in a subset of the class can be computed efficiently.

Discrete Applied Mathematics, 1993

Bibelnieks, E. and P.M. Dearing, Neighborhood subtree tolerance graphs, Discrete Applied Mathemat... more Bibelnieks, E. and P.M. Dearing, Neighborhood subtree tolerance graphs, Discrete Applied Mathematics 43 (1993) 13-26. In this paper, we introduce neighborhood subtree tolerance (NeST) graphs which are defined in terms of the tolerance-intersection of neighborhood subtrees of a tree. This class of graphs extends the class of interval tolerance graphs which are defined in terms of the tolerance-intersection of intervals on the real line. Interval tolerance graphs were first introduced by Golumbic and Monma as tolerance graphs. Some relationships among interval tolerance, NeST, and weakly triangulated graphs are examined. The main result shows that NeST graphs are weakly triangulated graphs. In addition, proper NeST graphs are shown to be exactly bounded NeST graphs and NeST graphs with constant tolerance are shown to be strongly chordal.

Operations Research Letters, 2009

A dual type algorithm constructs the minimum covering ball of a given finite set of points in R n... more A dual type algorithm constructs the minimum covering ball of a given finite set of points in R n by finding the minimum covering balls of a sequence of subsets, each with no more than n + 1 points and with strictly increasing radius, until all points are covered. (P.M. Dearing). center, without violating the covering property, until optimality is reached. Elzinga and Hearn [4] developed a dual approach in which the minimum covering circle is found for a sequence of subsets S ⊆ P, each of at most 3 points and with increasing radius, until some circle covers the entire set P. Other approaches use Voronoi diagrams . Meggido [6] developed a theoretical linear time algorithm for solving the problem.

Transportation Science, 1974

Transportation Science is the foremost journal in the field of transportation analysis, featuring... more Transportation Science is the foremost journal in the field of transportation analysis, featuring comprehensive, timely articles and surveys that cover all levels of planning and all modes of transportation. It is a quarterly journal published by the Institute for Operations Research and ...

Transportation Science, 1992

Operations Research, 1976

ABSTRACT

Operations Research, 1983

This paper investigates a class of single-facility location problems on an arbitrary network. Nec... more This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.

Journal of Global Optimization, 2013

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given... more The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in IR n is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration.

IIE Transactions, 1987

... and Implentation Depanment. bought on the outside market, finished at the Calhoun Mill ... On... more ... and Implentation Depanment. bought on the outside market, finished at the Calhoun Mill ... One approach to the above situation is to develop a linear programming model to maxim~ze profit subject to the re-quirements that demand he met and that loom capacity not be exceeded. ...

Annals of Operations Research, 2005

... They can also be viewed as a generalization of distances in fixed orientations as introduced ... more ... They can also be viewed as a generalization of distances in fixed orientations as introduced inWidmayer, Wu, and Wong (1987) where it is assumed that all ... from an origin point, xo = (xo, yo)T to a destination point xd = (xd, yd)T , denoted P(xo,xd), is a rectifiable, Jordan arc (see ...

Discrete Applied Mathematics, 1988

An algorithm for finding maximal chordal subgraphs is developed that has worst-case time complexi... more An algorithm for finding maximal chordal subgraphs is developed that has worst-case time complexity of O(IE(B), where IEI is the number of edges in G and d is the maximum vertex degree in G. The study of maximal chordal subgraphs is motivated by their usefulness as computationally efficient structures with which to approximate a general graph. Two examples are given that illustrate potential applications of maximal chordal subgraphs. One provides an alternative formulation to the maximum independent set problem on a graph. The other involves a novel splitting scheme for solving large sparse systems of linear equations.