Dynamic Programming Algorithm (dynamic + programming_algorithm)

Distribution by Scientific Domains


Selected Abstracts


Sequence alignment on the Cray MTA-2,

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 9 2004
Shahid H. Bokhari
Abstract Several variants of standard algorithms for DNA sequence alignment have been implemented on the Cray Multithreaded Architecture-2 (MTA-2). We describe the architecture of the MTA-2 and discuss how its hardware and software enable efficient implementation of parallel algorithms with little or no regard for issues of partitioning, mapping or scheduling. We describe how we ported variants of the naive algorithm for exact alignment and the dynamic programming algorithm for approximate alignment to the MTA-2 and provide detailed performance measurements. It is shown that, for the dynamic programming algorithm, the use of the MTA's ,Full/Empty' synchronization bits leads to almost perfect speedup for large problems on one to eight processors. These results illustrate the versatility of the MTA's architecture and demonstrate its potential for providing a high-productivity platform for parallel processing. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Resource allocation in satellite networks: certainty equivalent approaches versus sensitivity estimation algorithms

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2005
Franco Davoli
Abstract In this paper, we consider a resource allocation problem for a satellite network, where variations of fading conditions are added to those of traffic load. Since the capacity of the system is finite and divided in finite discrete portions, the resource allocation problem reveals to be a discrete stochastic programming one, which is typically NP-hard. We propose a new approach based on the minimization over a discrete constraint set using an estimation of the gradient, obtained through a ,relaxed continuous extension' of the performance measure. The computation of the gradient estimation is based on the infinitesimal perturbation analysis technique, applied on a stochastic fluid model of the network. No closed-forms of the performance measure, nor additional feedback concerning the state of the system, and very mild assumptions on the probabilistic properties about the statistical processes involved in the problem are requested. Such optimization approach is compared with a dynamic programming algorithm that maintains a perfect knowledge about the state of the satellite network (traffic load statistics and fading levels). The comparison shows that the sensitivity estimation capability of the proposed algorithm allows to maintain the optimal resource allocation in dynamic conditions and it is able to provide even better performance than the one reached by employing the dynamic programming approach. Copyright © 2004 John Wiley & Sons, Ltd. [source]


A travelling salesman problem with allocation, time window and precedence constraints , an application to ship scheduling

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2000
K. Fagerholt
Abstract A Travelling Salesman Problem with Allocation, Time Window and Precedence Constraints (TSP-ATWPC) is considered. The TSP-ATWPC occurs as a subproblem of optimally sequencing a given set of port visits in a real bulk ship scheduling problem, which is a combined multi-ship pickup and delivery problem with time windows and multi-allocation problem. Each ship in the fleet is equipped with a flexible cargo hold that can be partitioned into several smaller holds in a given number of ways, thus allowing multiple products to be carried simultaneously by the same ship. The allocation constraints of the TSP-ATWPC ensure that the partition of the ship's flexible cargo hold and the allocation of cargoes to the smaller holds are feasible throughout the visiting sequence. The TSP-ATWPC is solved as a shortest path problem on a graph whose nodes are the states representing the set of nodes in the path, the last visited node and the accumulated cargo allocation. The arcs of the graph represent transitions from one state to another. The algorithm is a forward dynamic programming algorithm. A number of domination and elimination tests are introduced to reduce the state space. The computational results show that the proposed algorithm for the TSP-ATWPC works, and optimal solutions are obtained to the real ship scheduling problem. [source]


A segmentation-based approach for temporal analysis of software version repositories,

JOURNAL OF SOFTWARE MAINTENANCE AND EVOLUTION: RESEARCH AND PRACTICE, Issue 3 2008
Harvey Siy
Abstract Time series segmentation is a promising approach to discover temporal patterns from time-stamped numeric data. A novel approach to apply time series segmentation to discern temporal information from software version repositories is proposed. Data from such repositories, both numeric and non-numeric, are represented as item-set time series data. A dynamic programming algorithm for optimal segmentation is presented. The algorithm automatically produces a compacted item-set time series that can be analyzed to identify temporal patterns. The effectiveness of the approach is illustrated by analyzing version control repositories of several open-source projects to identify time-varying patterns of developer activity. The experimental results show that the segmentation algorithm produces segments that capture meaningful information and is superior to the information content obtained by arbitrarily segmenting software history into regular time intervals. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Scheduling a maintenance activity on parallel identical machines

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 1 2009
Asaf Levin
Abstract We study a problem of scheduling a maintenance activity on parallel identical machines, under the assumption that all the machines must be maintained simultaneously. One example for this setting is a situation where the entire system must be stopped for maintenance because of a required electricity shut-down. The objective is minimum flow-time. The problem is shown to be NP-hard, and moreover impossible to approximate unless P = NP. We introduce a pseudo-polynomial dynamic programming algorithm, and show how to convert it into a bicriteria FPTAS for this problem. We also present an efficient heuristic and a lower bound. Our numerical tests indicate that the heuristic provides in most cases very close-to-optimal schedules. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source]


Deterministic and stochastic scheduling with teamwork tasks

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2004
Xiaoqiang Cai
Abstract We study a class of new scheduling problems which involve types of teamwork tasks. Each teamwork task consists of several components, and requires a team of processors to complete, with each team member to process a particular component of the task. Once the processor completes its work on the task, it will be available immediately to work on the next task regardless of whether the other components of the last task have been completed or not. Thus, the processors in a team neither have to start, nor have to finish, at the same time as they process a task. A task is completed only when all of its components have been processed. The problem is to find an optimal schedule to process all tasks, under a given objective measure. We consider both deterministic and stochastic models. For the deterministic model, we find that the optimal schedule exhibits the pattern that all processors must adopt the same sequence to process the tasks, even under a general objective function GC = F(f1(C1), f2(C2), , , fn(Cn)), where fi(Ci) is a general, nondecreasing function of the completion time Ci of task i. We show that the optimal sequence to minimize the maximum cost MC = max fi(Ci) can be derived by a simple rule if there exists an order f1(t) , , , fn(t) for all t between the functions {fi(t)}. We further show that the optimal sequence to minimize the total cost TC = , fi(Ci) can be constructed by a dynamic programming algorithm. For the stochastic model, we study three optimization criteria: (A) almost sure minimization; (B) stochastic ordering; and (C) expected cost minimization. For criterion (A), we show that the results for the corresponding deterministic model can be easily generalized. However, stochastic problems with criteria (B) and (C) become quite difficult. Conditions under which the optimal solutions can be found for these two criteria are derived. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004 [source]


Analysis of algorithms for two-stage flowshops with multi-processor task flexibility

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 1 2004
George L. Vairaktarakis
Abstract In this article we introduce a 2-machine flowshop with processing flexibility. Two processing modes are available for each task: namely, processing by the designated processor, and processing simultaneously by both processors. The objective studied is makespan minimization. This production environment is encountered in repetitive manufacturing shops equipped with processors that have the flexibility to execute orders either individually or in coordination. In the latter case, the product designer exploits processing synergies between two processors so as to execute a particular task much faster than a dedicated processor. This type of flowshop environment is also encountered in labor-intensive assembly lines where products moving downstream can be processed either in the designated assembly stations or by pulling together the work teams of adjacent stations. This scheduling problem requires determining the mode of operation of each task, and the subsequent scheduling that preserves the flowshop constraints. We show that the problem is ordinary NP-complete and obtain an optimal solution using a dynamic programming algorithm with considerable computational requirements for medium and large problems. Then, we present a number of dynamic programming relaxations and analyze their worst-case error performance. Finally, we present a polynomial time heuristic with worst-case error performance comparable to that of the dynamic programming relaxations. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source]


An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2003
Katerina P. Papadaki
We address the problem of dispatching a vehicle with different product classes. There is a common dispatch cost, but holding costs that vary by product class. The problem exhibits multidimensional state, outcome and action spaces, and as a result is computationally intractable using either discrete dynamic programming methods, or even as a deterministic integer program. We prove a key structural property for the decision function, and exploit this property in the development of continuous value function approximations that form the basis of an approximate dispatch rule. Comparisons on single product-class problems, where optimal solutions are available, demonstrate solutions that are within a few percent of optimal. The algorithm is then applied to a problem with 100 product classes, and comparisons against a carefully tuned myopic heuristic demonstrate significant improvements. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 742,769, 2003. [source]


Scheduling of depalletizing and truck loading operations in a food distribution system

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2003
Zhi-Long Chen
Abstract This paper studies a scheduling problem arising in a beef distribution system where pallets of various types of beef products in the warehouse are first depalletized and then individual cases are loaded via conveyors to the trucks which deliver beef products to various customers. Given each customer's demand for each type of beef, the problem is to find a depalletizing and truck loading schedule that fills all the demands at a minimum total cost. We first show that the general problem where there are multiple trucks and each truck covers multiple customers is strongly NP-hard. Then we propose polynomial-time algorithms for the case where there are multiple trucks, each covering only one customer, and the case where there is only one truck covering multiple customers. We also develop an optimal dynamic programming algorithm and a heuristic for solving the general problem. By comparing to the optimal solutions generated by the dynamic programming algorithm, the heuristic is shown to be capable of generating near optimal solutions quickly. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003 [source]


A dynamic programming algorithm for the conditional covering problem on tree graphs

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2005
Jennifer A. Horne
Abstract In a previous article, we presented algorithms for solving the Conditional Covering Problem (CCP) on path and extended star graphs. The CCP on these graphs can be solved in O(n2) time, where n is the number of nodes in the graph. In this article, we propose a new dynamic programming procedure to solve the CCP on tree graphs. This recursion works from the leaf nodes of the tree up to the root node, using notions of protected and unprotected costs as done for the CCP path algorithm in our previous work. We introduce new preliminary routines and data structures to merge information from subpaths and subtrees, resulting in an O(n4) algorithm to optimally solve the problem. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(4), 186,197 2005 [source]


Solving partial constraint satisfaction problems with tree decomposition

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2002
Arie M. C. A. Koster
Abstract In this paper, we describe a computational study to solve hard partial constraint satisfaction problems (PCSPs) to optimality. The PCSP is a general class of problems that contains a diversity of problems, such as generalized subgraph problems, MAX-SAT, Boolean quadratic programs, and assignment problems like coloring and frequency planning. We present a dynamic programming algorithm that solves PCSPs based on the structure (tree decomposition) of the underlying constraint graph. With the use of dominance and bounding techniques, we are able to solve small and medium-size instances of the problem to optimality and to obtain good lower bounds for large-size instances within reasonable time and memory limits. © 2002 Wiley Periodicals, Inc. [source]


A differential dynamic programming algorithm for differential games

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2001
Theodore B. Trafalis
Abstract We develop and prove the convergence of a first-order differential dynamic programming algorithm for the solution of a zero-sum two-person differential game with perfect information. The algorithm extends a first-order strong variation algorithm for optimal control given by Mayne and Polak. Assuming separability of the Hamiltonian, we decompose the differential game problem into two control subproblems, C1 and C2. The objective is to determine a point (u*, v*) in U×V, where U and V are the control spaces for C1 and C2, respectively, that satisfies an integral form of Pontryagin's maximum principle for differential games. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Using Image and Curve Registration for Measuring the Goodness of Fit of Spatial and Temporal Predictions

BIOMETRICS, Issue 4 2004
Cavan Reilly
Summary Conventional measures of model fit for indexed data (e.g., time series or spatial data) summarize errors in y, for instance by integrating (or summing) the squared difference between predicted and measured values over a range of x. We propose an approach which recognizes that errors can occur in the x -direction as well. Instead of just measuring the difference between the predictions and observations at each site (or time), we first "deform" the predictions, stretching or compressing along the x -direction or directions, so as to improve the agreement between the observations and the deformed predictions. Error is then summarized by (a) the amount of deformation in x, and (b) the remaining difference in y between the data and the deformed predictions (i.e., the residual error in y after the deformation). A parameter, ,, controls the tradeoff between (a) and (b), so that as ,,, no deformation is allowed, whereas for ,= 0 the deformation minimizes the errors in y. In some applications, the deformation itself is of interest because it characterizes the (temporal or spatial) structure of the errors. The optimal deformation can be computed by solving a system of nonlinear partial differential equations, or, for a unidimensional index, by using a dynamic programming algorithm. We illustrate the procedure with examples from nonlinear time series and fluid dynamics. [source]