Journal ArticleDOI
The Molecule Problem: Exploiting Structure in Global Optimization
TLDR
This paper presents a novel divide-and-conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones, and describes an implementation and some results of its performance on a sample molecule.Abstract:
The molecule problem is that of determining the relative locations of a set of objects in Euclidean space relying only upon a sparse set of pairwise distance measurements. This NP-hard problem has applications in the determination of molecular conformation. The molecule problem can be naturally expressed as a continuous, global optimization problem, but it also has a rich combinatorial structure. This paper investigates how that structure can be exploited to simplify the optimization problem. In particular, we present a novel divide-and-conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones. Since the cost of the optimization can grow exponentially with problem size, this approach holds the promise of a substantial improvement in performance. Our algorithmic development relies upon some recently published results in graph theory. We describe an implementation of this algorithm and report some results of its performance on a sample molecule.read more
Citations
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Convex analysis approach to d.c. programming: Theory, Algorithm and Applications
Tao Pham Dinh,Hoai An Le Thi +1 more
TL;DR: A thorough study on convex analysis approach to d.C.c. (difierence of convex functions) programming and gives the State of the Art results and the application of the DCA to solving a lot of important real-life d.c., polyhedral programming problems.
Journal ArticleDOI
A Theory of Network Localization
James Aspnes,Tolga Eren,David K. Goldenberg,A.S. Morse,Walter Whiteley,Yang Yang,Brian D. O. Anderson,Peter N. Belhumeur +7 more
TL;DR: This paper constructs grounded graphs to model network localization and applies graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks, and further study the computational complexity of network localization.
Proceedings ArticleDOI
Rigidity, computation, and randomization in network localization
Tolga Eren,O.K. Goldenberg,Walter Whiteley,Yang Yang,A.S. Morse,Brian D. O. Anderson,Peter N. Belhumeur +6 more
TL;DR: This work provides a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors and constructs grounded graphs to model network localization.
Journal ArticleDOI
Connected rigidity matroids and unique realizations of graphs
Bill Jackson,Tibor Jordán +1 more
TL;DR: It is deduced that every realization of a 6-connected graph as a two-dimensional generic framework is a unique realization, based on a new inductive characterization of 3-connected graphs whose rigidity matroid is connected.
Proceedings ArticleDOI
Graph rigidity and distributed formation stabilization of multi-vehicle systems
TL;DR: In this article, a graph theoretical framework is proposed to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations, as well as formal representation of split, rejoin, and reconfiguration maneuvers for multi-vehicle formations.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Book
Simulated Annealing: Theory and Applications
TL;DR: Performance of the simulated annealing algorithm and the relation with statistical physics and asymptotic convergence results are presented.
Journal ArticleDOI
Computing a Trust Region Step
Jorge J. Moré,Danny C. Sorensen +1 more
TL;DR: An algorithm for the problem of minimizing a quadratic function subject to an ellipsoidal constraint is proposed and it is shown that this algorithm is guaranteed to produce a nearly optimal solution in a finite number of iterations.
Journal ArticleDOI
On graphs and rigidity of plane skeletal structures
TL;DR: In this paper, the combinatorial properties of rigid plane skeletal structures are investigated, and the properties are found to be adequately described by a class of graph-structured graphs.
Journal ArticleDOI
Dividing a Graph into Triconnected Components
TL;DR: An algorithm for dividing a graph into triconnected components is presented and is both theoretically optimal to within a constant factor and efficient in practice.