Christine T. Cheng

Generating small combinatorial test suites to cover input-output relationships

In this paper, we consider a problem that arises in black box testing: generating small test suites (i.e., sets of test cases) where the combinations that have to be covered are specified by input-output parameter relationships of a software system. That is, we only consider combinations of input parameters that affect an output parameter. We also do not assume that the input parameters have the same number of values. To solve this problem, we revisit the greedy algorithm for test generation and show that the size of the test suite it generates is within a logarithmic factor of the optimal. Unfortunately, the algorithms main weaknesses are its time and space requirements for construction. To address this issue, we present a problem reduction technique that makes the greedy algorithm or any other test suite generation method more efficient if the reduction in size is significant.

From discrepancy to declustering: near-optimal multidimensional declustering strategies for range queries

Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Given a declustering scheme <i>D,</i> its <i>response time</i> with respect to a query <i>Q,</i> <i>rt</i>(<i>Q</i>), is defined to be the maximum number of disk blocks of the query stored by the scheme in any one of the disks. If |<i>Q</i>| is the number of data blocks in <i>Q</i> and <i>M</i> is the number of disks then <i>rt</i>(<i>Q</i>) is at least |<i>Q</i>|/<i>M.</i> One way to evaluate the performance of <i>D</i> with respect to a set of queries 𝑄 is to measure its <i>additive error</i> - the maximum difference between <i>rt</i>(<i>Q</i>) from |<i>Q</i>|/<i>M</i> over all range queries <i>Q</i> ε 𝑄.In this paper, we consider the problem of designing declustering schemes for uniform multidimensional data arranged in a <i>d</i>-dimensional grid so that their additive errors with respect to range queries are as small as possible. It has been shown that such declustering schemes will have an additive error of Ω(log <i>M</i>) when <i>d</i> = 2 and Ω(log d-1/2 <i>M</i>) when <i>d</i> > 2 with respect to range queries.Asymptotically optimal declustering schemes exist for 2-dimensional data. For data in larger dimensions, however, the best bound for additive errors is <i>O</i>(<i>M^d-1</i>), which is extremely large. In this paper, we propose the two declustering schemes based on low discrepancy points in <i>d</i>-dimensions. When <i>d</i> is fixed, both schemes have an additive error of <i>O</i>(log<i>^d-1 M</i>) with respect to range queries provided certain conditions are satisfied: the first scheme requires <i>d</i> ≥ 3 and <i>M</i> to be a power of a prime where the prime is at least <i>d</i> while the second scheme requires the size of the data to grow within some polynomial of <i>M,</i> with no restriction on <i>M.</i> These are the first known multidimensional declustering schemes with additive errors near optimal.

Replication and retrieval strategies of multidimensional data on parallel disks

Aside from enhancing data availability during disk failures, replication of data is also used to speed up I/O performance of read-intensive applications. There are two issues that need to be addressed: (a) data placement (Which disks should store the copies of each data block?) and (b) scheduling (Given a query Q, and a placement scheme P of the data, from which disk should each block in Q be retrieved so that retrieval time is minimized?) In this paper, we consider range queries and assume that the dataset is a multidimensional grid and r copies of each unit block of the grid must be stored among M disks. To accurately measure performance of a scheduling algorithm, we consider a metric that takes into account the scheduling overhead as well as the time it takes to retrieve the data blocks from the disks. We describe several combinations of data placement schemes and scheduling algorithms and analyze their performance for range queries with respect to the above metric. We then present simulation results for the most interesting case r=2, showing that the strategies do perform better than the previously known method, especially for large queries.

On Computing the Distinguishing Numbers of Planar Graphs and Beyond: A Counting Approach

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Improved Approximation Algorithms for the Demand Routing and Slotting Problem with Unit Demands on Rings

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From discrepancy to declustering: Near-optimal multidimensional declustering strategies for range queries

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On the local distinguishing numbers of cycles

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Understanding the Generalized Median Stable Matchings

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A unified approach to finding good stable matchings in the hospitals/residents setting

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Hardness results on the man-exchange stable marriage problem with short preference lists

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