algorithms for determining quality/cost/price tradeoffs in saturated markets are considered. A product is modeled by d real-valued qualities whose sum determines the unit cost of producing the product. This leads to t...
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algorithms for determining quality/cost/price tradeoffs in saturated markets are considered. A product is modeled by d real-valued qualities whose sum determines the unit cost of producing the product. This leads to the following optimization problem: given a set of n customers, each of whom has certain minimum quality requirements and a maximum price they are willing to pay, design a new product and select a price for that product in order to maximize the resulting profit. An O(nlog n) time algorithm is given for the case, d=1, of products having a single quality, and O(n(log n) (d+1)) time approximation algorithms are given for products with any constant number, d, of qualities. To achieve the latter result, an O(nk (d-1)) bound on the complexity of an arrangement of homothetic simplices in a"e (d) is given, where k is the maximum number of simplices that all contain a single points.
Computational methods and tools that can efficiently and effectively analyze the temporal changes in dynamic complex relational networks enable us to gain significant insights regarding the entity relations and their ...
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Computational methods and tools that can efficiently and effectively analyze the temporal changes in dynamic complex relational networks enable us to gain significant insights regarding the entity relations and their evolution. This article introduces a new class of dynamic graph patterns, referred to as coevolving relational motifs (CRMs), which are designed to identify recurring sets of entities whose relations change in a consistent way over time. CRMs can provide evidence to the existence of, possibly unknown, coordination mechanisms by identifying the relational motifs that evolve in a similar and highly conserved fashion. We developed an algorithm to efficiently analyze the frequent relational changes between the entities of the dynamic networks and capture all frequent coevolutions as CRMs. Our algorithm follows a depth-first exploration of the frequent CRM lattice and incorporates canonical labeling for redundancy elimination. Experimental results based on multiple real world dynamic networks show that the method is able to efficiently identify CRMs. In addition, a qualitative analysis of the results shows that the discovered patterns can be used as features to characterize the dynamic network.
Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph (MCG) problem is to find a connected subgraph with R vertices that maximizes the sum of the weights. The MCG probl...
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Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph (MCG) problem is to find a connected subgraph with R vertices that maximizes the sum of the weights. The MCG problem is strongly NP-complete, and we study a special case of it: the constrained MCG(CMCG) problem, which is the MCG problem with a constraint of having a predetermined vertex included in the solution. We first show that the Steiner tree problem is a special case of the CMCG problem. Then we present three optimization algorithms for the CMCG problem. The first two algorithms deal with special graphs (tree and layered graphs) and employ different dynamic programming techniques, solving the CMCG problem in polynomial times. The third one deals with a general graph and uses a variant of the Balas additive method with an imbedded connectivity test and a pruning method. We also present a heuristic algorithm for the CMCG problem with a general graph and its bound analysis. We combine the two algorithms, heuristic and optimization, and present a practical solution method to the CMCG problem. Computational results are reported and future research issues are discussed. (C) 1996 John Wiley & Sons, Inc.
We consider several programs used to tune PI/PID controllers based on transient characteristics of control systems;the tuning procedure does not require approximation by the corresponding analytical solution. We demon...
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We consider several programs used to tune PI/PID controllers based on transient characteristics of control systems;the tuning procedure does not require approximation by the corresponding analytical solution. We demonstrate that such programs can be downloaded from Internet.
A succinct introduction to splines, explaining how and why B-splines are used as a basis and how cubic and quadratic splines may be constructed, is followed by brief account of Hermite interpolation and Pade approxima...
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A succinct introduction to splines, explaining how and why B-splines are used as a basis and how cubic and quadratic splines may be constructed, is followed by brief account of Hermite interpolation and Pade approximations.
For finding global approximate solutions to an algebraic equation in n unknowns, the Hadamard open polygon for the case n = 1 and Hadamard polyhedron for the case n = 2 are used. The solutions thus found are transform...
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For finding global approximate solutions to an algebraic equation in n unknowns, the Hadamard open polygon for the case n = 1 and Hadamard polyhedron for the case n = 2 are used. The solutions thus found are transformed to the coordinate space by a translation (for n = 1) and by a change of coordinates that uses the curve uniformization (for n = 2). Next, algorithms for the local solution of the algebraic equation in the vicinity of its singular (critical) point for obtaining asymptotic expansions of one-dimensional and two-dimensional branches are presented for n = 2 and n = 3. Using the Newton polygon (for n = 2), the Newton polyhedron (for n = 3), and power transformations, this problem is reduced to situations similar to those occurring in the implicit function theorem. In particular, the local analysis of solutions to the equation in three unknowns leads to the uniformization problem of a plane curve and its transformation to the coordinate axis. Then, an asymptotic expansion of a part of the surface under examination can be obtained in the vicinity of this axis. Examples of such calculations are presented.
Radiation hybrid ( RH) mapping is a technique for constructing a physical map describing the locations of n markers on a chromosome of an organism. In [J. Comput. Biol., 4 (1997), pp. 517-533], Ben-Dor and Chor presen...
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Radiation hybrid ( RH) mapping is a technique for constructing a physical map describing the locations of n markers on a chromosome of an organism. In [J. Comput. Biol., 4 (1997), pp. 517-533], Ben-Dor and Chor presented new algorithms for the RH problem and gave the first performance guarantees for such algorithms. We improve the lower bounds on the number of experiments in a way that is sufficient for two of these algorithms to give a correct ordering of the markers with high probability. Not only are the new bounds tighter, but our analysis also captures to a much higher extent how the bounds depend on the actual arrangement of the markers. Furthermore, we modify the two algorithms to utilize RH mapping data produced with several radiation intensities. We show that the new algorithms are almost insensitive to the problem of using the correct intensity.
We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system...
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We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system consisting of N disks d(1), d(2),..., d(N). We are also given sets U-1, U-2,..., U-M such that U-i is the set of clients seeking the ith data item. Data item i has size si. Each disk d(j) is characterized by two parameters, namely, its storage capacity C-j which indicates the maximum total size of data items that may be assigned to it, and a load capacity L-j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data items to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system. We study this data placement problem for homogeneous storage systems where all the disks are identical. We assume that all disks have a storage capacity of and a load capacity of L. Previous work on this problem has assumed that all data items have unit size, in other words s(i) = 1 for all i. Even for this case, the problem is NP-hard. For the case where Si is an element of {1, . . . , Delta} for some constant Delta, we develop a polynomial time approximation scheme (PTAS). This result is obtained by developing two algorithms, one that works for constant k and one that works for arbitrary k. The algorithm for arbitrary k guarantees that a solution where at least ((k - Delta)/(k + Delta)) (1 - 1/(1 + root k/(2 Delta))(2))- fraction of all clients are assigned to a disk (under certain assumptions). In addition we develop an algorithm for which we can prove tight bounds when s(i) is an element of {1, 2}. In fact, we can show that a (1 - 1/(1 + root L[k/2])(2))-fraction of all clients can be assigned (under certain natural assumptions), regardless of the input distribution. (c) 2004 Elsevier Inc. All tights reserved.
Sliding mode control (SMC) is among the popular approaches for control of systems, especially for unknown nonlinear systems. However, the chattering in SMC is generally a problem that needs to be resolved for better c...
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Sliding mode control (SMC) is among the popular approaches for control of systems, especially for unknown nonlinear systems. However, the chattering in SMC is generally a problem that needs to be resolved for better control. A time-varying method is proposed for determining the sliding gain function in the SMC. Two alternative tuning algorithms are proposed for reducing the sliding gain function for systems. The first algorithm is for systems with no noise and disturbance but with or without unmodeled dynamics. The second algorithm is for systems with noise, disturbance, unmodeled dynamics, or any combination of them. Compared with the state-dependent, equivalent-control-dependent, and hysteresis loop methods, the proposed algorithms are more straightforward and easy to implement. The performance of the algorithms is evaluated for five different cases. A 90% to 95% reduction of chattering is achieved for the first algorithm used for systems with sensor dynamics only. By using the second algorithm, the chattering is reduced by 70% to 90% for systems with noise and/or disturbance, and by 25% to 50% for systems with a combination of disturbance, noise, and unmodeled dynamics. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
In the 2-CLUB CLUSTER VERTEX DELETION (resp., 2-CLUB CLUSTER EDGE DELETION) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices (resp., edges) whose ...
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In the 2-CLUB CLUSTER VERTEX DELETION (resp., 2-CLUB CLUSTER EDGE DELETION) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices (resp., edges) whose removal from G results in a graph in which the diameter of every connected component is at most 2. In this paper we give algorithms for 2-CLUB CLUSTER VERTEX DELETION and 2-CLUB CLUSTER EDGE DELETION whose running times are O*(3.104k) and O*(2.562k), respectively. Our algorithms were obtained using automated generation of branching rules. Our results improve the previous O*(3.303k)-time algorithm for 2-CLUB CLUSTER VERTEX DELETION [Liu et al., FAW-AAIM 2012] and the O*(2.695k)-time algorithm for 2-CLUB CLUSTER EDGE DELETION [Abu-Khzam et al., TCS 2023].
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