14478113
Sequencing jobs that require common resources on a single machine: A solvable case of the TSP
In this paper a one-machine scheduling model is analyzed wheren different jobs are classified intoK groups depending on which additional resource they require. The change-over time from one job to another consists of the removal time or of the set-up time of the two jobs. It is sequence-dependent in the sense that the change-over time is determined by whether or not the two jobs belong to the same group. The objective is to minimize the makespan. This problem can be modeled as an asymmetric Traveling Salesman Problem (TSP) with a specially structured distance matrix. For this problem we give a polynomial time solution algorithm that runs in O(n logn) time. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
96314
On the long-step path-following method for semidefinite programming
It has been shown in various recent research reports that the analysis of short-step primal-dual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long-step path-following algorithms for semidefinite programming appeared to be less straightforward. For such an algorithm, Monteiro (1997) obtained an O(n^1^.^5log(1/@e)) iteration bound for obtaining an @e-optimal solution, where n is the order of the semidefinite decision variable. In this paper, we propose to use a different search direction, viz. the so-called V-space direction. It is shown that this modification reduces the iteration complexity to O(nlog(1/@e)). Independently, Monteiro and Y. Zhang obtained a similar result using Nesterov-Todd directions.
16330147
A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming
This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.
17355776
A deep cut ellipsoid algorithm for convex programming: Theory and applications
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.
12742018
On Cones of Nonnegative Quadratic Functions
We derive linear matrix inequality (LMI) characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for instance the intersection of a (upper) level-set of a quadratic function and a half-plane. Consequently, we arrive at a generalization of Yakubovich's S-procedure result. Although the primary concern of this paper is to characterize the matrix cones by LMIs, we show, as an application of our results, that optimizing a general quadratic function over the intersection of an ellipsoid and a half-plane can be formulated as semidefinite programming (SDP), thus proving the polynomiality of this class of optimization problems, which arise, e.g., from the application of the trust region method for nonlinear programming. Other applications are in control theory and robust optimization.
3196759
Low-complexity algorithms for sequencing jobs with a fixed number of job-classes
In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold.
6304926
Identifying bridging rules between conceptual clusters
A bridging rule in this paper has its antecedent and action from different conceptual clusters. We first design two algorithms for mining bridging rules between clusters in a database, and then propose two non-linear metrics for measuring the interestingness of bridging rules. Bridging rules can be distinct from association rules (or frequent itemsets). This is because (1) bridging rules can be generated by infrequent itemsets that are pruned in association rule mining; and (2) bridging rules are measured by the importance that includes the distance between two conceptual clusters, whereas frequent itemsets are measured by only the support.
29457354
A novel shape matching method using biological sequence dynamic alignment
Shape description and its corresponding matching algorithm is one of the main concerns in MPEG-7. A novel dynamic shape matching algorithm is proposed. First, the conventional 8-directional chain code is exploited to describe the binary shape. A dynamic shape matching algorithm, which is derived from the solution for the biological sequence similarity analysis based on molecular evolutionary theory, is proposed to measure the similarity distance between the shapes by computing their similarity score (SS). Based on a large set of MPEG-7 binary shapes, simulation results have shown that the proposed dynamic alignment matching algorithm is fairly promising and also robust to scale changes, small non-rigid deformation, and similarity based shape matching defined in MPEG-7 core experiments.
6709890
An agent-based hybrid framework for database mining
While knowledge discovery in databases (KDD) is defined as an iterative sequence of the following steps: data pre-processing, data mining, and post data mining, a significant amount of research in data mining has been done, resulting in a variety of algorithms and techniques for each step. However, a single data-mining technique has not been proven appropriate for every domain and data set. Instead, several techniques may need to be integrated into hybrid systems and used cooperatively during a particular data-mining operation. That is, hybrid solutions are crucial for the success of data mining. This paper presents a hybrid framework for identifying patterns from databases or multi-databases. The framework integrates these techniques for mining tasks from an agent point of view. Based on the experiments conducted, putting different KDD techniques together into the agent-based architecture enables them to be used cooperatively when needed. The proposed framework provides a highly flexible and robust data-mining platform and the resulting systems demonstrate emergent behaviors although it does not improve the performance of individual KDD techniques.
1204298
An implicit degree condition for long cycles in 2-connected graphs
Abstract Let id ( v ) denote the implicit degree of a vertex v . In this work we prove that: If G is a 2-connected graph with max { id ( u ) , id ( v ) } ≥ c / 2 for each pair of nonadjacent vertices u and v that are vertices of an induced claw or an induced modified claw of G , then G contains either a Hamilton cycle or a cycle of length at least c . This extends several previous results on the existence of long cycles in graphs.
11213421
Consensus Folding of Unaligned RNA Sequences Revisited
As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.