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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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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 (4 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...
Techniques for highly multiobjective optimisation: Some nondominated points are better than others
 in Proceedings GECCO 2007. ACM
, 2007
"... The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly ..."
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The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly when problems have ‘many ’ (e.g. five or more) objectives. One of the chief reasons for this is believed to be that, in manyobjective EMO search, populations are likely to be largely composed of nondominated solutions. In turn, this means that the commonlyused algorithms cannot distinguish between these for selective purposes. However, there are methods that can be used validly to rank points in a nondominated set, and may therefore usefully underpin selection in EMO search. Here we discuss and compare several such methods. Our main finding is that simple variants of the oftenoverlooked ‘Average Ranking ’ strategy usually outperform other methods tested, covering problems with 5—20 objectives and differing amounts of interobjective correlation. Categories and Subject Descriptors I.2.8 [Problem solving, control methods and search]: Heuristic methods
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
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...
Eliciting matters  controlling skyline sizes by incremental integration of user preferences
 In Proceedings of the 12th International Conference on Database Systems for Advanced Applications (DASFAA
, 2007
"... Abstract. Today, result sets of skyline queries are unmanageable due to their exponential growth with the number of query predicates. In this paper we discuss the incremental recomputation of skylines based on additional information elicited from the user. Extending the traditional case of totally ..."
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Cited by 11 (4 self)
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Abstract. Today, result sets of skyline queries are unmanageable due to their exponential growth with the number of query predicates. In this paper we discuss the incremental recomputation of skylines based on additional information elicited from the user. Extending the traditional case of totally ordered domains, we consider preferences in their most general form as strict partial orders of attribute values. After getting an initial skyline set our basic approach aims at interactively increasing the system’s information about the user’s wishes explicitly including indifferences. The additional knowledge then is incorporated into the preference information and constantly reduces skyline sizes. In fact, our approach even allows users to specify tradeoffs between different query predicates, thus effectively decreasing the query dimensionality. We give theoretical proof for the soundness and consistence of the extended preference information and an extensive experimental evaluation of the efficiency of our approach. On average, skyline sizes can be considerably decreased in each elicitation step.