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Algorithms and Analyses for Maximal Vector Computation
"... The maximal vector problem is to identify the maximals over a collection of vectors. This arises in many contexts and, as such, has been well studied. The problem recently gained renewed attention with skyline queries for relational databases and with work to develop skyline algorithms that are exte ..."
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Cited by 24 (0 self)
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The maximal vector problem is to identify the maximals over a collection of vectors. This arises in many contexts and, as such, has been well studied. The problem recently gained renewed attention with skyline queries for relational databases and with work to develop skyline algorithms that are external and relationally well behaved. While many algorithms have been proposed, how they perform has been unclear. We study the performance of, and design choices behind, these algorithms. We prove runtime bounds based on the number of vectors n and the dimensionality k. Early algorithms based on divideandconquer established seemingly good average and worstcase asymptotic runtimes. In fact, the problem can be solved in O(n) averagecase (holding k as fixed). We prove, however, that the performance is quite bad with respect to k. We demonstrate that the more recent skyline algorithms are better behaved, and can also achieve O(kn) averagecase. While k matters for these, in practice, its effect vanishes in the asymptotic. We introduce a new external algorithm, LESS, that is more efficient and better behaved. We evaluate LESS’s effectiveness and improvement over the field, and prove that its averagecase running time is O(kn). 1
Towards Multidimensional Subspace Skyline Analysis
"... The skyline operator is important for multicriteria decisionmaking applications. Although many recent studies developed efficient methods to compute skyline objects in a given space, none of them considers skylines in multiple subspaces simultaneously. More importantly, the fundamental ..."
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Cited by 17 (3 self)
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The skyline operator is important for multicriteria decisionmaking applications. Although many recent studies developed efficient methods to compute skyline objects in a given space, none of them considers skylines in multiple subspaces simultaneously. More importantly, the fundamental
V.G.: “Delay optimization of carryskip adders and block carrylookahead adders
 Proc. of Int’l Symposium on Computer Arithmetic
, 1991
"... AbstractThe worstcase carry propagation delays in carryskip adders and block carrylookahead adders depend on how the full adders are grouped structurally together into blocks as well as the number of levels. We report on a multidimensional dynamic programming paradigm for configuring these two ad ..."
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Cited by 15 (1 self)
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AbstractThe worstcase carry propagation delays in carryskip adders and block carrylookahead adders depend on how the full adders are grouped structurally together into blocks as well as the number of levels. We report on a multidimensional dynamic programming paradigm for configuring these two adders to attain minimum latency. Previous methods are applicable only to very limited delay models that do not guarantee a minimum latency configuration. Under our delay model, critical path delay is calculated not only taking into account the intrinsic gate delays, but also the fanin and fanout contributions. Index TermsBlock carrylookahead adders, carryskip adders, CMOS, computer arithmetic, delay optimization, multidimensional dynamic programming, VLSI design.
On the Complexity of QoS Routing
 Computer Communications
, 2003
"... We present SAMCRA, an exact QoS routing algorithm that guarantees to find a feasible path if such a path exists. Because SAMCRA is an exact algorithm, its complexity also characterizes that of QoS routing in general. The complexity of SAMCRA is simulated in specific classes of graphs. Since the comp ..."
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Cited by 14 (3 self)
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We present SAMCRA, an exact QoS routing algorithm that guarantees to find a feasible path if such a path exists. Because SAMCRA is an exact algorithm, its complexity also characterizes that of QoS routing in general. The complexity of SAMCRA is simulated in specific classes of graphs. Since the complexity of an algorithm involves a scaling of relevant parameters, the second part of this paper analyses how routing with multiple independent link weights affects the hopcount distribution. Both the complexity and the hopcount analysis indicate that for a special class of networks, QoS routing exhibits features similar to singleparameter routing. These results suggest that there may exist classes of graphs in which QoS routing is not NPcomplete.
Computing Optimal Rectilinear Steiner Trees: A Survey and Experimental Evaluation
 Discrete Applied Mathematics
, 1998
"... The rectilinear Steiner tree problem is to find a minimumlength rectilinear interconnection of a set of points in the plane. A reduction from the rectilinear Steiner tree problem to the graph Steiner tree problem allows the use of exact algorithms for the graph Steiner tree problem to solve the rec ..."
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Cited by 13 (2 self)
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The rectilinear Steiner tree problem is to find a minimumlength rectilinear interconnection of a set of points in the plane. A reduction from the rectilinear Steiner tree problem to the graph Steiner tree problem allows the use of exact algorithms for the graph Steiner tree problem to solve the rectilinear problem. Furthermore, anumber of more direct, geometric algorithms have been devised for computing optimal rectilinear Steiner trees. This paper surveys algorithms for computing optimal rectilinear Steiner trees and presents experimental results comparing nine of them: graph Steiner tree algorithms due to Beasley, Bern, Dreyfus and Wagner, Hakimi, and Shore, Foulds, and Gibbons and geometric algorithms due to Ganley and Cohoon, Salowe and Warme, and Thomborson, Alpern, and Carter. 1 Introduction The rectilinear Steiner tree (RST) problem is stated as follows: given a set T of n points called terminals in the plane, find a set S of additional points called Steiner points such tha...
Efficient Algorithms for Computing the Maximum Distance Between Two Finite Planar Sets
 Journal of Algorithms
, 1983
"... An O(n log n) algorithm is presented for computing the maximum euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity can be reduced to O(n). The algorithm is empirically compared to the bruteforce method as well as an a ..."
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Cited by 11 (6 self)
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An O(n log n) algorithm is presented for computing the maximum euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity can be reduced to O(n). The algorithm is empirically compared to the bruteforce method as well as an alternate O(n 2 ) algorithm. Both the O(n log n) and O(n 2 ) algorithms run in O(n) expected time for many underlying distributions of the points. An eapproximate algorithm can be obtained that runs in O(n + 1/e) worstcase time. 1. Introduction Let S 1 = p 1 , p 2 ,..., p n and S 2 = q 1 , q 2 ,..., q n be two planar sets of n points, and let S = S 1 È S 2 . (The sets need not have equal cardinality, but this assumption simplifies notation.) A point p i is given by the cartesian coordinates x i and y i . The maximum distance between S 1 and S 2 , denoted by d max (S 1 , S 2 ), is defined as d max (S 1 , S 2 ) = {d(p i ,q j )}, i, j = 1,2,...,n, where d(p i ,q j ) is the euclidean dista...
Counting colors in boxes
 In Proceedings of Symposium on Discrete Algorithms (SODA
, 2007
"... Let P be a set of n points in R d, so that each point is colored by one of C given colors. We present algorithms for preprocessing P into a data structure that efficiently supports queries of the form: Given an axisparallel box Q, count the number of distinct colors of the points of P ∩ Q. We prese ..."
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Cited by 11 (1 self)
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Let P be a set of n points in R d, so that each point is colored by one of C given colors. We present algorithms for preprocessing P into a data structure that efficiently supports queries of the form: Given an axisparallel box Q, count the number of distinct colors of the points of P ∩ Q. We present a general and relatively simple solution that has polylogarithmic query time and worstcase storage about O(n d). It is based on several interesting structural properties of the problem that we derive. We also show that for random inputs, the data structure requires almost linear expected storage. We then present several techniques for achieving spacetime tradeoff. In R 2, the most efficient solution uses fast matrix multiplication in the preprocessing stage. In higher dimensions we use simpler tradeoff mechanisms, which behave just as well. We give a reduction from matrix multiplication to the offline version of problem, which shows that in R 2 our timespace tradeoffs are close to optimal in the sense that improving them substantially would improve the best exponent of matrix multiplication. Finally, we present a generalized matrix multiplication problem and show its intimate relation to counting colors in boxes in any dimension. 1
Skyline with presorting: Theory and optimization
 In Int. Inf. Sys. Conference (IIS
, 2005
"... Abstract. There has been interest recently in skyline queries, also called Pareto queries, on relational databases. Relational query languages do not support search for “best ” tuples, beyond the order by statement. The proposed skyline operator allows one to query for best tuples with respect to an ..."
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Cited by 11 (3 self)
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Abstract. There has been interest recently in skyline queries, also called Pareto queries, on relational databases. Relational query languages do not support search for “best ” tuples, beyond the order by statement. The proposed skyline operator allows one to query for best tuples with respect to any number of attributes as preferences. In this work, we explore what the skyline means, and why skyline queries are useful, particularly for expressing preference. We describe the theoretical aspects and possible optimizations of an efficiant algorithm for computing skyline queries presented in [6]. 1
Exploiting Indifference for Customization of Partial Order Skylines
 INT. DATABASE ENGINEERING AND APPLICATIONS SYMP. (IDEAS
, 2006
"... Unlike numerical preferences, preferences on attribute values do not show an inherent total order, but skyline computation has to rely on partial orderings explicitly stated by the user. In such orders many object values are incomparable, hence skylines sizes become unpractical. However, the Pareto ..."
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Cited by 10 (4 self)
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Unlike numerical preferences, preferences on attribute values do not show an inherent total order, but skyline computation has to rely on partial orderings explicitly stated by the user. In such orders many object values are incomparable, hence skylines sizes become unpractical. However, the Pareto semantics can be modified to benefit from indifferences: skyline result sizes can be essentially reduced by allowing the user to declare some incomparable values as equally desirable. A major problem of adding such equivalences is that they may result in intransitivity of the aggregated Pareto order and thus efficient query processing is hampered. In this paper we analyze how far the strict Pareto semantics can be relaxed while always retaining transitivity of the induced Pareto aggregation. Extensive practical tests show that skyline sizes can indeed be reduced about two orders of magnitude when using the maximum possible relaxation still guaranteeing the consistency with all user preferences.