Erscheinungsdatum: 03/2012, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Optimum Partition Parameter of Divide-And-Conquer Algorithm, Titelzusatz: Solving Closest-Pair Problem, Autor: Karim, Mohammad Zaidul // Akter, Nargis, Verlag: LAP Lambert Academic Publishing, Sprache: Englisch, Rubrik: Technik // Sonstiges, Seiten: 76, Informationen: Paperback, Gewicht: 130 gr, Verkäufer: averdo
Optimum Partition Parameter of Divide-And-Conquer Algorithm ab 49 € als Taschenbuch: Solving Closest-Pair Problem. Aus dem Bereich: Bücher, Wissenschaft, Technik,
Optimum Partition Parameter of Divide-And-Conquer Algorithm ab 49 EURO Solving Closest-Pair Problem
In this book we investigate methods to solve certain inverse problems. According to Hadamard a problem is well-posed if a unique solution exists and the solution depends continuously on the data. If one of these properties is not fulfilled a problem is calledill-posed. Typically an inverse problem is ill-posed. In many applications it may not be necessary to solve the inverse problemin detail. One is only interested in determining areas, which differ in certain physical properties to a reference condition. For example in nondestructive material tests one is looking for holes, cracks or inclusions in a matter. Such partition of the domain in inclusion and surrounding area is called binary segmentation. In this work we study three different methods for solving such binary inverse problems.
The minimum k-partition (MkP) problem is the problemof partitioning the set of vertices of a graph into kdisjoint subsets so as to minimize the total weightof the edges joining vertices in the same partition.The main contribution is the design andimplementation of a novel iterative clusteringheuristic (ICH) based on semide nite programming to nd feasible solutions for the MkP problem. Wecompare ICH to the hyperplane rounding techniques,and the computational results support the conclusionthat ICH consistently provides better feasiblesolutions for the MkP problem. We use ICH in abranch-and-cut algorithm to provide feasiblesolutions at each node of the branch-and-bound tree.The branch-and-cut algorithm computes globallyoptimal solutions for dense graphs with up to 60vertices, for grid graphs with up to 100 vertices,and for different values of k, providing the bestexact approach to date for k 2.
A many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases (Gaussian field theory, 1D Ising model). The n-body system is replaced by a 1-body problem with a chosen good external field. The external field replaces the interaction of all the other particles to an arbitrary particle. The great difficulty (e.g. when computing the partition function of the system) is the treatment of combinatorics generated by the interaction terms in the Hamiltonian when summing over all states. The goal of mean field theory (MFT, also known as self-consistent field theory) is to resolve these combinatorial problems. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction. This reduces any multi-body problem into an effective one-body problem. The ease of solving MFT problems means that some insight into the behavior of the system can be obtained at a relatively low cost. In field theory, the Hamiltonian may be expanded in terms of the magnitude of fluctuations around the mean of the field.
This book considres one the main problems in discrete mathematics which is called the classification problem. In such a problem, given a collection of properties, construct up to isomorphism all structures that satisfy them. In otherwords, the classification problem is the problem of determining complete systems of representatives of the isomorphism classes. Also, this book considers both the use of invariants and the use of partition backtracking for solving the isomorphism problems of 0,1-matrices, in general. It also discusses the inverse problem of finding all structures for a given invariant. This leads to the composition principle for incidence structures and eventually to some new results. The goal of this book is to be of great help to researchers. Also, it can be used for graduate courses in both mathematics and computer sciences.