44823536
A class of web-based facets for the generalized vertex packing problem
The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges. This paper derives a class of valid inequalities based on certain special subgraphs called webs, which are general structures that subsume cliques, matchings, odd holes, and odd anti-holes. We also provide a set of conditions for this class of valid inequalities to be facet-inducing for the web subgraph polytope. Finally, we prescribe a web subgraph identification procedure, and test the computational benefits obtained by solving generalized vertex packing instances with formulations augmented by these web-based valid inequalities.
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.
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
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
10698762
Exact and heuristic algorithms for solving the generalized minimum filter placement problem
We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model.
44866557
A Multiple-Criterion Model for Machine Scheduling
We consider a scheduling problem involving a single processor being utilized by two or more customers. Traditionally, such scenarios are modeled by assuming that each customer has the same criterion. In practice, this assumption may not hold. Instead of using a single criterion, we examine the implications of minimizing an aggregate scheduling objective function in which jobs belonging to different customers are evaluated based on their individual criteria. We examine three basic scheduling criteria: minimizing makespan, minimizing maximum lateness, and minimizing total weighted completion time. Although determining a minimum-cost schedule according to any one of these criteria is polynomially solvable, we demonstrate that when minimizing a mix of these criteria, the problem becomes NP-hard.
45728102
Causal Identification in Design Networks
When planning and designing a policy intervention and evaluation, the policy maker will have to define a strategy which will define the (conditional independence) structure of the available data. Here, Dawid’s extended influence diagrams are augmented by including ‘experimental design’ decisions nodes within the set of intervention strategies to provide semantics to discuss how a ‘design’ decision strategy (such as randomisation) might assist the systematic identification of intervention causal effects. By introducing design decision nodes into the framework, the experimental design underlying the data available is made explicit. We show how influence diagrams might be used to discuss the efficacy of different designs and conditions under which one can identify ‘causal’ effects of a future policy intervention. The approach of this paper lies primarily within probabilistic decision theory.
7567156
Optimized Encodings of Fragments of Type Theory in First Order Logic
The paper presents sound and complete translations of several fragments of Martin-Lof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gandalf and several experimental results are described.
7794743
Efficient, automatic web resource harvesting
There are two problems associated with conventional web crawling techniques: a crawler cannot know if all resources at a non-trivial web site have been discovered and crawled ("the counting problem") and the human-readable format of the resources are not always suitable for machine processing ("the representation problem"). We introduce an approach that solves these two problems by implementing support for both the Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH) and MPEG-21 Digital Item Declaration Language (DIDL) into the web server itself. We present the Apache module "mod_oai", which can be used to address the counting problem by listing all valid URIs at a web server and efficiently discovering updates and additions on subsequent crawls. Our experiments indicated comparable performance for initial crawls, and dramatic increases in update speed mod_oaican also be used to address the representation problem by providing "preservation ready" versions of web resources aggregated with their respective forensic metadata in MPEG-21 DIDL format.
6106969
Service-Based Distributed Querying on the Grid
Service-based approaches (such as Web Services and the Open Grid Services Architecture) have gained considerable attention recently for supporting distributed application development in e-business and e-science. The emergence of a service-oriented view of hardware and software resources raises the question as to how database management systems and technologies can best be deployed or adapted for use in such an environment. This paper explores one aspect of service-based computing and data management, viz., how to integrate query processing technology with a service-based Grid. The paper describes in detail the design and implementation of a service-based distributed query processor for the Grid. The query processor is service-based in two orthogonal senses: firstly, it supports querying over data storage and analysis resources that are made available as services, and, secondly, its internal architecture factors out as services the functionalities related to the construction of distributed query plans on the one hand, and to their execution over the Grid on the other. The resulting system both provides a declarative approach to service orchestration in the Grid, and demonstrates how query processing can benefit from dynamic access to computational resources on the Grid.
17447930
Incorporation of adaptive mutation based on subjective evaluation in an interactive evolution strategy
A rapidly emerging model in the field of adaptive computing is the symbiosis of human expertise with evolutionary algorithms for user controlled and directed search. The two aspects in any EA are the selection of individuals to reproduce based on some measure of their quality or fitness and the application of variation operators to produce new solutions. In the context of interactive evolution, these aspects are compounded by the need for rapid convergence to prevent user fatigue and to provide the user some control over the generation of new solutions. Elsewhere, in the work of the authors (2004), we have examined different policies for best incorporating the user into the evaluation and selection process. In this paper, we explore the hypothesis that user assigned fitness represents a source of information that can be used to control the variation process: effectively to broaden the search if none of the current solutions is promising, or focus the search and improve convergence speed in the vicinity of a good solution. The main aims of this study, therefore, are to analyse the advantages of using a user directed adaptive mutation strategy over fixed mutation step sizes in terms of time to converge and robustness of the resulting solution. We present results showing a qualitatively different type of search process can be obtained by using the user assigned fitness to control the nature of the mutation process. There is also a synergy between user-based selection and fitness-based mutation control which out performs either system on its own.