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Marked Ancestor Problems
, 1998
"... Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path. ..."
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Cited by 52 (7 self)
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Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path.
Fast Algorithm for Creating Space Efficient Dispatching Tables with Application to MultiDispatching
 In Proceedings of the 17 th Annual Conference on ObjectOriented Programming Systems, Languages, and Applications
, 2002
"... The dispatching problem can be solved very efficiently in the singleinheritance (SI) setting. In this paper we show how to extend one such solution to the multipleinheritance (MI) setting. This generalization comes with an increase to the space requirement by a small factor of . This factor can ..."
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Cited by 13 (4 self)
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The dispatching problem can be solved very efficiently in the singleinheritance (SI) setting. In this paper we show how to extend one such solution to the multipleinheritance (MI) setting. This generalization comes with an increase to the space requirement by a small factor of . This factor can be thought of as a metric of the complexity of the topology of the inheritance hierarchy.
UNIFYING THE LANDSCAPE OF CELLPROBE LOWER BOUNDS
, 2008
"... We show that a large fraction of the datastructure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: • highdimensional problems, where the goal is to show large space lower bounds. • co ..."
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Cited by 11 (0 self)
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We show that a large fraction of the datastructure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: • highdimensional problems, where the goal is to show large space lower bounds. • constantdimensional geometric problems, where the goal is to bound the query time for space O(n·polylogn). • dynamic problems, where we are looking for a tradeoff between query and update time. (In this case, our bounds are slightly weaker than the originals, losing a lglgn factor.) Our reductions also imply the following new results: • an Ω(lgn/lglgn) bound for 4dimensional range reporting, given space O(n · polylogn). This is quite timely, since a recent result [39] solved 3D reporting in O(lg 2 lgn) time, raising the prospect that higher dimensions could also be easy. • a tight space lower bound for the partial match problem, for constant query time. • the first lower bound for reachability oracles. In the process, we prove optimal randomized lower bounds for lopsided set disjointness.
Incremental Algorithms for Dispatching in Dynamically Typed Languages
"... A fundamental problem in the implementation of objectoriented languages is that of a frugal dispatching data structure, i.e., support for quick response to dispatching queries combined with compact representation of the type hierarchy and the method families. Previous theoretical algorithms tend to ..."
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Cited by 4 (3 self)
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A fundamental problem in the implementation of objectoriented languages is that of a frugal dispatching data structure, i.e., support for quick response to dispatching queries combined with compact representation of the type hierarchy and the method families. Previous theoretical algorithms tend to be impractical due to their complexity and large hidden constant. In contrast, successful practical heuristics, including Vitek and Horspool's compact dispatch tables (CT) [16] designed for dynamically typed languages, lack theoretical support. In subjecting CT to theoretical analysis, we are not only able to improve and generalize it, but also provide the first nontrivial bounds on the performance of such a heuristic.
Pattern Matching in Trees and Strings
, 2007
"... The work presented in this dissertation was done while I was enrolled as a PhD student at the IT University of Copenhagen in the 4year PhD program. My work was funded by the EUproject ”Deep Structure, Singularities, and Computer Vision ” (IST Programme of the European Union (IST200135443)). Duri ..."
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Cited by 3 (0 self)
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The work presented in this dissertation was done while I was enrolled as a PhD student at the IT University of Copenhagen in the 4year PhD program. My work was funded by the EUproject ”Deep Structure, Singularities, and Computer Vision ” (IST Programme of the European Union (IST200135443)). During the summer of 2003 my advisors Stephen Alstrup and Theis Rauhe left to start their own company and my advisors then became Lars Birkedal and Anna Östlin Pagh. In the period from March 2003 to September 2003 I was on paternity leave. I received my Masters Degree in January 2005. In Spring 2005 I visited Martin FarachColton at Rutgers University twice for a total period of two months. In the period from October 2006 to April 2007 I was on another 6 months of paternity leave. Finally, in the remaining period I came back to finish the present dissertation. I want to thank all of the inspiring people that I have worked with during my PhD. In particular, I want to thank Stephen Alstrup and Theis Rauhe for introducing me to their unique perspective on algorithms. I also want to thank Lars Birkedal, Anna Östlin Pagh, and Rasmus Pagh for tons of guidance. I am grateful to Martin FarachColton for the very pleasant stay at Rutgers University. Thanks to all of my coauthors:
Time and space efficient multimethod dispatching
 IN SWAT: SCANDINAVIAN WORKSHOP ON ALGORITHM THEORY
, 2002
"... ..."
The architecture of a software library for string processing
, 1997
"... We present our project to develop a software library of basic tools and data structures for string processing. Our goal is to provide an environment for testing new algorithms as well as for prototyping. The library has a natural hierarchy comprising basic objects such as the alphabet and strings, d ..."
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Cited by 2 (0 self)
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We present our project to develop a software library of basic tools and data structures for string processing. Our goal is to provide an environment for testing new algorithms as well as for prototyping. The library has a natural hierarchy comprising basic objects such as the alphabet and strings, data structures to manipulate these objects, and powerful algorithmic techniques driving these data structures. Furthermore, it has the natural taxonomy imposed by the underlying string processing tasks (such as static/dynamic, offline/online, exact/approximate). We believe that our architecture presents a unified view of string processing encompassing recently developed techniques and insights this may be of independent interest to those who seek an introduction to this field. Our design is preliminary and we hope to refine it based on feedback.
Lower Bound Techniques for Data Structures
, 2008
"... We describe new techniques for proving lower bounds on datastructure problems, with the following broad consequences:
â¢ the first Î©(lgn) lower bound for any dynamic problem, improving on a bound that had been standing since 1989;
â¢ for static data structures, the first separation between linea ..."
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Cited by 1 (0 self)
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We describe new techniques for proving lower bounds on datastructure problems, with the following broad consequences:
â¢ the first Î©(lgn) lower bound for any dynamic problem, improving on a bound that had been standing since 1989;
â¢ for static data structures, the first separation between linear and polynomial space. Specifically, for some problems that have constant query time when polynomial space is allowed, we can show Î©(lg n/ lg lg n) bounds when the space is O(n Â· polylog n).
Using these techniques, we analyze a variety of central datastructure problems, and obtain improved lower bounds for the following:
â¢ the partialsums problem (a fundamental application of augmented binary search trees);
â¢ the predecessor problem (which is equivalent to IP lookup in Internet routers);
â¢ dynamic trees and dynamic connectivity;
â¢ orthogonal range stabbing;
â¢ orthogonal range counting, and orthogonal range reporting;
â¢ the partial match problem (searching with wildcards);
â¢ (1 + Îµ)approximate near neighbor on the hypercube;
â¢ approximate nearest neighbor in the lâ metric.
Our new techniques lead to surprisingly nontechnical proofs. For several problems, we obtain simpler proofs for bounds that were already known.
Web www.itc.dkTime and Space Efficient MultiMethod Dispatching
, 2001
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy.
An Optimal Dynamic Data Structure for StabbingSemigroup Queries ∗
"... Let S be a set of n intervals in R, and let (S,+) be any commutative semigroup. We assign a weight ω(s) ∈ S to each interval in S. For a point x ∈ R, let S(x) ⊆ S be the set of intervals that contain x. Given a point q ∈ R, the stabbingsemigroup query asks for ω(s). We propose a linearsize dynam ..."
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Let S be a set of n intervals in R, and let (S,+) be any commutative semigroup. We assign a weight ω(s) ∈ S to each interval in S. For a point x ∈ R, let S(x) ⊆ S be the set of intervals that contain x. Given a point q ∈ R, the stabbingsemigroup query asks for ω(s). We propose a linearsize dynamic data structure, under the pointermachine model, that answers queries in worstcaseO(logn) time, and supports both insertions and deletions of intervals in amortized O(logn) time. It is the first data structure that attains the optimal O(logn) bound for all three operations. Furthermore, our structure can easily be adapted to external memory, where we obtain a linearsize structure that answers queries and supports updates inO(logB n) I/Os, where B is the disk block size. For the restricted case of nested family of intervals (every pair of intervals are either disjoint or one contains the other), we present a simpler solution based on dynamic trees. computing ∑ s∈S(q) 1