Browsing by Subject "clustering"

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Open Access
Row generation techniques for approximate solution of linear programming problems
(2010) Paç, A. Burak
In this study, row generation techniques are applied on general linear programming problems with a very large number of constraints with respect to the problem dimension. A lower bound is obtained for the change in the objective value caused by the generation of a specific row. To achieve row selection that results in a large shift in the feasible region and the objective value at each row generation iteration, the lower bound is used in the comparison of row generation candidates. For a warm-start to the solution procedure, an effective selection of the subset of constraints that constitutes the initial LP is considered. Several strategies are discussed to form such a small subset of constraints so as to obtain an initial solution close to the feasible region of the original LP. Approximation schemes are designed and compared to make possible the termination of row generation at a solution in the proximity of an optimal solution of the input LP. The row generation algorithm presented in this study, which is enhanced with a warm-start strategy and an approximation scheme is implemented and tested for computation time and the number of rows generated. Two efficient primal simplex method variants are used for benchmarking computation times, and the row generation algorithm appears to perform better than at least one of them especially when number of constraints is large.
Open Access
Storage and access schemes for aggregate query processing on road networks
(2009) Demir, Engin
A well-known example of spatial networks is road networks, which form an integral part of many geographic information system applications, such as locationbased services, intelligent traveling systems, vehicle telematics, and locationaware advertising. In practice, road network data is too large to fit into the volatile memory. A considerable portion of the data must be stored on the secondary storage since several spatial and non-spatial attributes as well as points-ofinterest data are associated with junctions and links. In network query processing, the spatial coherency that exists in accessing data leads to a temporal coherency; in this way, connected junctions are accessed almost concurrently. Taking this fact into consideration, it seems reasonable to place the data associated with connected junctions in the same disk pages so that the data can be fetched to the memory with fewer disk accesses. We show that the state-of-the-art clustering graph model for allocation of data to disk pages is not able to correctly capture the disk access cost of successor retrieval operations. We propose clustering models based on hypergraph partitioning, which correctly encapsulate the spatial and temporal coherency in query processing via the utilization of query logs in order to minimize the number of disk accesses during aggregate query processing. We introduce the link-based storage scheme for road networks as an alternative to the widely used junction-based storage scheme. We present GetUnevaluated-Successors (GUS) as a new successor retrieval operation for network queries, where the candidate successors to be retrieved are pruned during processing a query. We investigate two different instances of GUS operation: the Get-unProcessed-Successors operation typically arises in Dijkstra’s single source shortest path algorithm, and the Get-unVisited-Successors operation typically arises in the incremental network expansion framework. The simulation resultsshow that our storage and access schemes utilizing the proposed clustering hypergraph models are quite effective in reducing the number of disk accesses during aggregate query processing.