38357274
Algorithms for distributing telecommunication traffic on a multiple-ring SONET-based network
Abstract We examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network (SONET) rings. Prior SONET design algorithms determine node-to-ring assignments while concurrently prescribing an assignment of traffic to the rings. However, due to uncertain voice and data demand among client nodes, it may become necessary to revise the planned routing scheme once the true values of this data are realized. We develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings, and provide a transformation to a maximum flow problem for specially structured data. The case in which each demand pair may be routed on only one ring is proven to be NP-hard, and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits. The effectiveness of our approach is demonstrated on a set of randomly generated test data.
27619841
Dynamic programming algorithms for the conditional covering problem on path and extended star graphs
The Conditional Covering Problem (CCP) is a facility location problem on a graph, where the set of nodes represents demand points and potential facility locations. The key aspect of the CCP is that each facility covers all nodes within a given facility-specific coverage radius, except for the node at which it is located. The objective of this problem is to minimize the sum of the facility location costs required to cover all demand points. We first discuss the worst-case complexity of the CCP by examining literature related to the total domination problem, which is a special case of the CCP. Next, we examine the special case of path graphs and provide an O(n2) algorithm for its solution. Finally, we leverage information obtained from this procedure to derive an optimal algorithm for “extended star” graphs (multiple paths having one node in common), without increasing the worst-case complexity of the algorithm. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(4), 177–185 2005
40597287
A polyhedral study of the generalized vertex packing problem
The traditional vertex packing problem defined on an undirected graph identifies the largest weighted independent set of nodes, that is, a set of nodes whose induced subgraph contains no edges. In this paper, we examine a generalized vertex packing problem (GVP-k) in which k ``violations'' to the independent set restriction are permitted, whereby k edges may exist within the subgraph induced by the chosen set of nodes. A particular context in which such problems arise is in the national airspace planning model of Sherali, Smith, and Trani (2000), where a set of flight-plans need to be composed for various flights subject to conflict, workload, and equity considerations. The GVP-k structure arises in modeling the air-traffic control sector workload restrictions, which stipulate that for each sector and during each discretized time-slot, the number of aircraft conflicts that would need to be resolved should not exceed k, for some k≥1. We derive several classes of facetial valid inequalities for GVP-k for certain specially structured subgraphs, identifying polynomial-sized convex hull representations for some of these cases. Related constraint generation routines are also developed, and some computational results are provided to demonstrate the efficacy of utilizing the proposed valid inequalities in solving GVP-k for different values of k.
42617820
The Optimal Deployment of Filters to Limit Forged Address Attacks in Communication Networks
We consider forged address attacks in communication networks, wherein an attacking node forges the address of communication requests sent to a victim node. Unless the victim can ascertain the origin of the attack, it must cease to respond to communication requests until the attack subsides. We examine the problem of identifying a minimum cardinality subset of nodes on a network, such that placing route-based filters on these nodes provides a prescribed level of security. We model the problem as an integer program and illustrate its performance on randomly generated networks. Next, we develop a greedy heuristic to deploy filters in these networks, and compare its solution quality to that of the integer programming approach. These findings are then used to motivate both the importance of addressing this problem by optimal techniques and to motivate future research approaches for solving such problems.
18781640
An Analysis of the Alias Method for Discrete Random-Variate Generation
This paper introduces and studies an optimization problem related to the alias method for discrete random-variate generation. The alias method is an efficient method to generate random variates from a discrete probability distribution. The efficiency of the alias method can be improved by designing the alias table such that the expected number of computations that must be performed per value generated is minimized. The problem of optimizing the construction of the alias table is proven to be strongly NP-hard, even if either of two variations of the alias method relaxing the alias-table-generation restrictions are used. Integer-programming formulations describing these three optimization problems are presented, and insights regarding necessary optimality criteria and relationships among their optimal solutions are discussed.
106215
A stochastic integer programming approach to solving a synchronous optical network ring design problem
We develop stochastic integer programming techniques tailored toward solving a Synchronous Optical Network (SONET) ring design problem with uncertain demands. Our approach is based on an L-shaped algorithm, whose (integer) master program prescribes a candidate network design, and whose (continuous) subproblems relay information regarding potential shortage penalty costs to the ring design decisions. This naive implementation performs very poorly due to two major problems: (1) the weakness of the master problem relaxations, and (2) the limited information passed to the master problem by the optimality cuts. Accordingly, we enforce certain necessary conditions regarding shortage penalty contributions to the objective function within the master problem, along with a corresponding set of valid inequalities that improves the solvability of the master problem. We also show how a nonlinear reformulation of the model can be used to capture an exponential number of optimality cuts generated by the linear model. We augment these techniques with a powerful upper-bounding heuristic to further accelerate the convergence of the algorithm, and demonstrate the effectiveness of our methodologies on a test bed of randomly generated stochastic SONET instances. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 12–26 2004
40619191
The Design, Implementation and Evaluation of an ODMG Compliant, Parallel Object Database Server
This paper describes the design, implementation and evaluation of a parallel object database server. While a number of research groups and companies now provide object database servers designed to run on uniprocessors, there has been surprisingly little work on the exploitation of parallelism to provide scalable performance in Object Database Management Systems (ODBMS). The work described in this paper takes as its starting-point the Object Database Management Group (ODMG) standard for object databases, thereby allowing the project to focus on research into parallelism, rather than on the ODBMS interfaces. The system is designed to run on a distributed memory parallel machine, and the paper describes the key issues and design decisions including: parallel query optimisation and execution, flow control, support for user-defined operations in queries, object distribution, cache management and navigational client access. The work shows that the significant differences between the object and relational database paradigms lead to significant differences in the designs of parallel servers to support these two paradigms. The paper presents an extensive performance analysis of the prototype systems which shows that good performance can be achieved on a cluster of linux PCs.
6859122
Supporting Incremental Join Queries on Ranked Inputs
This paper investigates the problem of incremental joins of multiple ranked data sets when the join condition is a list of arbitrary user-defined predicates on the input tuples. This problem arises in many important applications dealing with ordered inputs and multiple ranked data sets, and requiring the top solutions. We use multimedia applications as the motivating examples but the problem is equally applicable to traditional database applications involving optimal resource allocation, scheduling, decision making, ranking, etc. We propose an algorithm that enables querying of ordered data sets by imposing arbitrary userdefined join predicates. The basic version of the algorithm does not use any random access but a variation can exploit available indexes for efficient random access based on the join predicates. A special case includes the join scenario considered by Fagin [1] for joins based on identical keys, and in that case, our algorithms perform as efficiently as Fagin’s. Our main contribution, however, is the generalization to join scenarios that were previously unsupported, including cases where random access in the algorithm is not possible due to lack of unique keys. In addition, can support multiple join levels, or nested join hierarchies, which are the norm for modeling multimedia data. We also give -approximation versions of both of the above algorithms. Finally, we give strong optimality results for some of the proposed algorithms, and we study their performance empirically.
16226748
Polar: an architecture for a parallel ODMG compliant object database
Object database management systems (ODBMS) are now established as the database management technology of choice for a range of challenging data intensiv e applications. Furthermore, the applications associated with object databases typically have stringen t performance requirements, and some are associated with very large data sets. Ho w ever, despite the demands made on object databases by applications, there has been surprisingly little work on parallel object databases. This paper presents the arc hitecture and some preliminary performance results for the Polar ODMG compliant parallel object database. The architecture described has been implemented in a shared-nothing environment on a network of PCs. The paper describes how OQL queries are compiled, parallelized and executed in this environment, and includes some preliminary performance results for OQL queries using the 007 benchmark.
17816721
Triangle Guarding
We consider the problem of triangle guarding ( -guarding) a simple, 2D polygon Q. A polygon Q is -guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards to lie in Q and Q has a transparent boundary then the vertices of the convex hull of Q (CH (Q)) form the minimum set of -guards. We examine two other variations of the problem. In the first, the guards may be placed within a transparent border surrounding Q. For this variation, we describe a polynomial time algorithm, related to the classic algorithm for finding min-link separators, that finds a minimum set of -guards. In the second, we consider the case where Q’s boundary is opaque and show that, as in the traditional art gallery problem, finding a minimum set of vertex -guards is NP-hard. Transparent Fences Given simple polygons P and Q with Q contained in P , where |Q|+ |P | = n, what is the minimum number and placement of guards in P needed to -guard Q, assuming that both Q and P have transparent boundaries? Our algorithm for this problem is inspired by an algorithm for finding min-link separators between two convex polygons, one contained in the other [1]. The following basic lemmas motivate using this approach. Define legal regions to be regions of the outer polygon P , that are not contained in the interior of CH (Q) (Figure 1).
17602182
Architecture of the artifact-based collaboration system matrix
The UNC Collaboratory project is concerned with both the process of collaboration and with computer systems to support that process. Here, we describe a component of the Artifact-Based Collaboration (ABC) system, called the Matrix, that provides an infrastructure in which existing single-user applications can be incorporated with few, if any, changes and used collaboratively. We take the position that what is needed is not new tools but better infrastructure for using familiar single-user tools collectively. The paper discusses the Matrix architecture, a Virtual Screen component, and generic functions that provide conferencing, hyperlinking, and recording of users' actions for all applications. INTRODUCTION AND MOTIVATION