Collette Coullard | Lake Superior State University (original) (raw)

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Papers by Collette Coullard

Lecture Notes in Computer Science, 2008

With the proliferation of wireless networks and mobile computing devices, providing location-awar... more With the proliferation of wireless networks and mobile computing devices, providing location-aware technology and services to new applications has become important for developers. Our main contribution is an efficient location discovery algorithm that bounds the localization error. Providing an efficient localization technique is critical in resource-constrained environments that include mobile devices and wireless networked sensors. Applicable in centralized and distributed environments, our algorithm, based on finding the smallest circle enclosing the intersection of n disks, runs in 2 ( ) O n time. We then extend our work to the problem of finding the smallest disk that includes the set of points common to n disks and excluded from the interiors of m other disks. Finally, we show performance results from the implementation of our algorithms in which, under some conditions, localization estimates for 500 nodes in a 500x500 ft region can be found with a mean error of one foot and a two-foot error bound.

Proceedings of HICSS-29: 29th Hawaii International Conference on System Sciences, 1996

ABSTRACT We survey three problem representations that are popularly applied in combinatorial opti... more ABSTRACT We survey three problem representations that are popularly applied in combinatorial optimization: algebraic modeling languages, constraint logic programming languages, and network diagrams. After first describing the kinds of optimization methods and systems most commonly associated with these alternatives, we consider how each representation has been advantageous and how its advantages have come to influence (or ought to influence) the design of the others. We focus especially on the possibility that general-purpose system designs, which are highly successful in other areas, might be extended to combinatorial optimization

A new necessary condition for a graph G to be the visibility graph of a simple polygon is given: ... more A new necessary condition for a graph G to be the visibility graph of a simple polygon is given: each 3connected component of G must. have a vertex ordering in which every vertex is adjacent to a previous 3-clique. This property is used to give an algorithm for the distance visibility graph problem: given an edge-weighted graph G, is it the visibility graph of a simple polygon with the given weights as Euclidean distances?

Linear Algebra and its Applications, 1995

A Leontief directed hypergraph is a generalization of a directed graph, where arcs have multiple ... more A Leontief directed hypergraph is a generalization of a directed graph, where arcs have multiple (or no) tails and at most one head. We define a class of Leontief directed hypergraphs via a forbidden structure called an odd pseudocycle. We show that the vertex-hyperarc incidence matrices of the hypergraphs in this class are totally unimodular. Indeed, we show that this is the largest class with that property. We define two natural subclasses of this class (one obtained by forbidding pseudocycles and the other obtained by forbidding pseudocycles and the so-called doublecycles), and we describe some structural properties of the bases and circuits of the members of these classes. We present examples of Leontief directed hypergraphs that are graphic, cographic, and neither graphic nor cographic.

Operations Research Letters, 1985

... Article Outline. • References. Volume 4, Number 2 OPERATIONS RESEARCH LETTERS July 1985 ON TH... more ... Article Outline. • References. Volume 4, Number 2 OPERATIONS RESEARCH LETTERS July 1985 ON THE COMPLEXITY OF RECOGNIZING A CLASS OF GENERALIZED NETWORKS Vijaya CHANDRU, * Collette R. COULLARD and ... [2] RE Bixby and DK Wagner, &quot;An almost ...

Linear Algebra and its Applications, 1989

Given an undirected graph C and a cost associated with each edge, the weighted girth problem is t... more Given an undirected graph C and a cost associated with each edge, the weighted girth problem is to find a simple cycle of G having minimum total cost. We consider several variants of the weighted girth problem, some of which are NP-hard and some of which are solvable in polynomial time. We also consider the polyhedra associated with each of these problems. Two of these polyhedra are the cycle cone of 6, which is the cone generated by the incidence vectors of cycles of 6, and the cycle polytope of G, which is the convex hull of the incidence vectors of cycles of 6. First we give a short proof of Seymour's characterization of the cycle cone of G. Next we give a polyhedral composition result for the cycle polytope of 6. In particular, we prove that if G decomposes via a 3-edge cut into graphs 6, and G,, say, then defining linear systems for the cycle polytopes of G, and G, can be combined in a certain way to obtain a defining linear system for the cycle polytope of G. We also describe a

Journal of Combinatorial Theory, Series B, 1992

Tutte's wheels-and-whirls theorem states that if M is a 3-connected matroid and, for every elemen... more Tutte's wheels-and-whirls theorem states that if M is a 3-connected matroid and, for every element e, both the deletion and the contraction of e destroy 3-connectivity, then it4 is a wheel or a whirl. We prove some extensions of this theorem, one of which states that if M is 3-connected and has both a wheel and a whirl minor, then either M has only seven elements or there is some element the deletion or contraction of which maintains 3connectivity and leaves a matroid with both a wheel and a whirl minor.

International Journal of Computational Geometry & Applications, 1992

Practical algorithmic methods for combinatorial optimization problems cannot be considered in iso... more Practical algorithmic methods for combinatorial optimization problems cannot be considered in isolation from the representations that people use when communicating these problems to computer systems. Di erent representations de ne di erent problem classes, for which distinct types of methods are appropriate. Conversely, di erent methods have di erent ranges of applicability, w h i c h h a ve motivated a diverse variety of representations.

Discrete Applied Mathematics, 1996

This paper presents a linear-inequality description of the dominant of the polytope of the 2-conn... more This paper presents a linear-inequality description of the dominant of the polytope of the 2-connected Steiner subgraphs of a given IV,-free graph. For the special case of 2-connected spanning subgraphs, a description of the polytope is given. The latter contains the Traveling-Salesman polytope for IV,-free graphs as a face.

Discrete Applied Mathematics, 1987

As introduced by Chv~ital, cutting planes provide a canonical way of proving that every integral ... more As introduced by Chv~ital, cutting planes provide a canonical way of proving that every integral solution of a given system of linear inequalities satisfies another specified inequality. In this note we make several observations on the complexity of such proofs in general and when restricted to proving the unsatisfiability of formulae in the propositional calculus. ** Supported by the joint research project "Algorithmic Aspects of Combinatorial Optimization" of the Hungarian Academy of Sciences (Magyar Tudom~inyos Akad6mia) and the German Research Association (Deutsche Forschungsgemeinschaft) and SFB 303 (DFG). 0166-218X/87/$3.50 © 1987, Elsevier Science Publishers B.V.