This special issue of algorithms is devoted to the study of matching problems involving ordinal preferences from the standpoint of algorithms and complexity.
This special issue of algorithms is devoted to the study of matching problems involving ordinal preferences from the standpoint of algorithms and complexity.
Capacity reservation contracts allow a consumer to purchase up to a certain capacity at a unit price lower than that of the spot market, while the consumer's excess orders are realized at the spot price. In this p...
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Capacity reservation contracts allow a consumer to purchase up to a certain capacity at a unit price lower than that of the spot market, while the consumer's excess orders are realized at the spot price. In this paper, we consider a lot sizing problem where the consumer places orders following a capacity reservation contract. In particular, we study the general problem and the polynomial time solvable special cases of the problem and propose corresponding algorithms for them. (C) 2013 Elsevier B.V. All rights reserved.
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive...
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This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components. (C) 2012 Elsevier B.V. All rights reserved.
We study the NP-hard Target Set Selection (TSS) problem occurring in social network analysis. Roughly speaking, given a graph where each vertex is associated with a threshold, in TSS the task is to select a minimum-si...
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We study the NP-hard Target Set Selection (TSS) problem occurring in social network analysis. Roughly speaking, given a graph where each vertex is associated with a threshold, in TSS the task is to select a minimum-size "target set'' such that all vertices of the graph get activated. Activation is a dynamic process. First, only the vertices in the target set are active. Then, a vertex becomes active if the number of its active neighbors exceeds its threshold, and so on. TSS models the spread of information, infections, and influence in networks. Complementing results on its polynomial-time approximability and extending results for its restriction to trees and bounded treewidth graphs, we classify the influence of the parameters "diameter'', "cluster editing number'', "vertex cover number'', and "eedback edge set number'' of the underlying graph on the problem's computational complexity, revealing both tractable and intractable cases. For instance, even for diameter-two split graphs TSS remains W[2]-hard with respect to the parameter "size of the target set''. TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixed-parameter tractable when parameterized by the vertex cover number. Both results contrast known parameterized intractability results for the parameter "treewidth''. While these tractability results are relevant for sparse networks, we also show efficient fixed-parameter algorithms for the parameter "cluster editing number'', yielding tractability for certain dense networks.
Algebraic and Geometric Ideas in the Theory of Discrete Optimization offers several research technologies not yet well known among practitioners of discrete optimization, minimizes prerequisites for learning these me...
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ISBN:
(数字)9781611972443
ISBN:
(纸本)9781611972436
Algebraic and Geometric Ideas in the Theory of Discrete Optimization offers several research technologies not yet well known among practitioners of discrete optimization, minimizes prerequisites for learning these methods, and provides a transition from linear discrete optimization to nonlinear discrete optimization.
We define a class of algebras over finite fields, called polynomially cyclic algebras, which extend the class of abelian field extensions. We study the structure of these algebras;furthermore, we define and investigat...
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We define a class of algebras over finite fields, called polynomially cyclic algebras, which extend the class of abelian field extensions. We study the structure of these algebras;furthermore, we define and investigate properties of Lagrange resolvents and Gauss and Jacobi sums. Natural examples of polynomially cyclic algebras are for instance algebras of the form F(p)[X]/(F(q)(X)) where p, q are distinct odd primes and F(q) is the q-th cyclotomic polynomial. Further examples occur similarly on replacing the cyclotomic polynomials with factors of division polynomials of elliptic curves. Finally, Gauss and Jacobi sums over polynomially cyclic algebras are applied for improving current algorithms for counting the number of points of elliptic curves over finite fields. (C) 2010 Published by Elsevier Ltd
In formal language theory, studying shortest strings in languages, and variations thereof, can be useful since these strings can serve as small witnesses for properties of the languages, and can also provide bounds fo...
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In formal language theory, studying shortest strings in languages, and variations thereof, can be useful since these strings can serve as small witnesses for properties of the languages, and can also provide bounds for other problems involving languages. For example, the length of the shortest string accepted by a regular language provides a lower bound on the state complexity of the *** Chapter 1, we introduce some relevant concepts and notation used in automata and language theory, and we show some basic results concerning the connection between the length of the shortest string and the nondeterministic state complexity of a regular language. Chapter 2 examines the effect of the intersection operation on the length of the shortest string in regular languages. A tight worst-case bound is given for the length of the shortest string in the intersection of two regular languages, and loose bounds are given for two variations on the problem. Chapter 3 discusses languages that are defined over a free group instead of a free monoid. We study the length of the shortest string in a regular language that becomes the empty string in the free group, and a variety of bounds are given for different cases. Chapter 4 mentions open problems and some interesting observations that were made while studying two of the problems: finding good bounds on the length of the shortest squarefree string accepted by a deterministic finite automaton, and finding an efficient way to check if a finite set of finite words generates the free monoid. Some of the results in this thesis have appeared in work that the author has participated in \cite{AngPigRamSha,AngShallit}
In this article we considered a kind of new location problem, The problem is to determine a path on the network to minimize the total weighted distance from it to n given point on the network. It is proved that the pr...
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ISBN:
(纸本)9781424472352
In this article we considered a kind of new location problem, The problem is to determine a path on the network to minimize the total weighted distance from it to n given point on the network. It is proved that the problem is *** the network is a tree,The problem is solved by polynomial-time algorithm, this algorithm complexity is O (n~2 ), then some approximate methods based on tree's situation are designed.
The polygon retrieval problem on points is the problem of preprocessing a set of n points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great i...
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The polygon retrieval problem on points is the problem of preprocessing a set of n points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such as Computer Graphics, CAD applications, Spatial Databases and GIS developing tasks. In this paper we study the problem of canonical k-vertex polygon queries on the plane. A canonical k-vertex polygon query always meets the following specific property: a point retrieval query can be transformed into a linear number (with respect to the number of vertices) of point retrievals for orthogonal objects such as rectangles and triangles (throughout this work we call a triangle orthogonal iff two of its edges are axis-parallel). We present two new algorithms for this problem. The first one requires O(n log(2) n) space and O(k log.n/loglogn + A) query time. A simple modification scheme on first algorithm lead us to a second solution, which consumes O(n(2)) space and O(k logn/loglogn + A) query time, where A denotes the size of the answer and k is the number of vertices. The best previous solution for the general polygon retrieval problem uses O(n(2)) space and answers a query in O(k log n + A) time, where k is the number of vertices. It is also very complicated and difficult to be implemented in a standard imperative programming language such as C or C++.
A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function ...
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A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph classes G, an (F, G)-system is a Boolean dynamical system such that all local transition functions lie in F and the underlying graph lies in G. Let F be a class of Boolean functions which is closed under composition and let G be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If F contains the self-dual functions and G contains the planar graphs, then the fixed-point existence problem for (F, G)-systems with local transition function given by truth-tables is NP-complete;otherwise, it is decidable in polynomial time. (2) If F contains the self-dual functions and G contains the graphs having vertex covers of size one, then the fixed-point existence problem for (F, G)-systems with local transition function given by formulas or circuits is NP-complete;otherwise, it is decidable in polynomial time.
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