Publications (26)3.9 Total impact
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ABSTRACT: We give an explicit representation for the offline optimum strategy for list update under the MRM model of Martínez and Roura [C. Martínez, S. Roura, On the competitiveness of the movetofront rule, Theoret. Comput. Sci. 242 (1–2) (2000) 3130–325] and Munro [J.I. Munro, On the competitiveness of linear search, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 338–345] and give an O(n3)O(n3) algorithm to compute it. This is in contrast to the standard model of Sleator and Tarjan [D.D. Sleator, R.E. Tarjan, Amortized efficiency of list update and paging rules, Commun. ACM 28 (2) (1985) 202–208] under which computing the offline optimum was shown to be NPhard [C. Ambühl, Offline list update is NPhard, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 42–51]. This algorithm follows from a new characterization theorem for realizable visiting sequences in the MRM model.Information Processing Letters 01/2012; 112:218222. · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of supporting Rank() and Select() operations on a bit vector of length m with n 1 bits. The problem is considered in the succinct index model, where the bit vector is stored in "readonly" memory and an additional data structure, called the index, is created during preprocessing to help answer the above queries. We give asymptotically optimal densitysensitive tradeoffs, involving both m and n, that relate the size of the index to the number of accesses to the bit vector (and processing time) needed to answer the above queries. The results are particularly interesting for the case where n = o(m).Algorithmica 08/2011; · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of sorting a permutation using a network of data structures as introduced by Knuth and Tarjan. In general the model as considered previously was restricted to networks that are directed acyclic graphs (DAGs) of stacks and/or queues. In this paper we study the question of which are the smallest general graphs that can sort an arbitrary permutation and what is their efficiency. We show that certain twonode graphs can sort in time Θ(n2) and no simpler graph can sort all permutations. We then show that certain threenode graphs sort in time Ω(n3/2), and that there exist graphs of k nodes which can sort in time Θ(nlogkn), which is optimal.Discrete Applied Mathematics 01/2010; · 0.72 Impact Factor 
Conference Paper: Cell probe lower bounds for succinct data structures.
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ABSTRACT: In this paper, we consider several static data structure problems in the deterministic cell probe model. We develop a new technique for proving lower bounds for succinct data structures, where the redundancy in the storage can be small compared to the information theoretic minimum. In fact, we succeed in matching (up to constant factors) the lower order terms of the existing data structures with the lower order terms provided by our lower bound. Using this technique, we obtain (i) the first lower bound for the problem of searching and retrieval of a substring in text; (ii) a cell probe lower bound for the problem of representing permutation π with queries π(i )a ndπ−1(i )t hat matches the lower order term of the existing data structures, and (iii) a lower bound for representing binary matrices that is also matches upper bounds for some set of parameters. The nature of all these problems is that we are to implement two operations that are in a reciprocal relation to each other (search and retrieval, computing forward and inverse element, operations on rows and columns of a matrix). As far as we know, this paper is the first to provide an insight into such problems.Proceedings of the Twentieth Annual ACMSIAM Symposium on Discrete Algorithms, SODA 2009, New York, NY, USA, January 46, 2009; 01/2009 
Conference Paper: On the Redundancy of Succinct Data Structures.
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ABSTRACT: The redundancy of a succinct data structure is the difference between the space it uses and the appropriate informationtheoretic lower bound. We consider the problem of representing binary sequences and strings succinctly using small redundancy. We improve the redundancy required to support the important operations of rank and select efficiently for binary sequences and for strings over small alphabets. We also show optimal densitysensitive upper and lower bounds on the redundancy for systematic encodings of binary sequences.Algorithm Theory  SWAT 2008, 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 24, 2008, Proceedings; 01/2008 
Conference Paper: On the Size of Succinct Indices.
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ABSTRACT: A succinct data structure occupies an amount of space that is close to the informationtheoretic minimum plus an additional term. The latter is not necessarily a lowerorder term and, in several cases, completely dominates the space occupancy both in theory and in practice. In this paper, we present several solutions to partially overcome this problem, introducing new techniques of independent interest that allow us to improve over previously known upper and lower bounds.Algorithms  ESA 2007, 15th Annual European Symposium, Eilat, Israel, October 810, 2007, Proceedings; 01/2007  Theor. Comput. Sci. 01/2007; 387:284297.
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ABSTRACT: The most heavily used methods to answer conjunctive queries on binary relations (such as the one associating keywords with web pages) are based on inverted lists stored in sorted arrays and use variants of binary search. We show that a succinct representation of the binary relation permits much better results, while using space within a lower order term of the optimal. We apply our results not only to conjunctive queries on binary relations, but also to queries on semistructured documents such as XML documents or filesystem indexes, using a variant of an adaptive algorithm used to solve conjunctive queries on binary relations. Keywordsconjunctive queriesintersection problemsuccinct data structureslabeled treesmultilabeled trees06/2006: pages 2435;  [Show abstract] [Hide abstract]
ABSTRACT: We develop a new lower bound technique for data structures. We show an optimal W(n lglgn / lgn)\Omega(n \lg\lg n / \lg n) space lower bounds for storing an index that allows to implement rank and select queries on a bit vector B provided that B is stored explicitly. These results improve upon [Miltersen, SODA’05]. We show W((m/t) lgt)\Omega((m/t) \lg t) lower bounds for storing rank/select index in the case where B has m 1bits in it (e.g. low 0th entropy) and the algorithm is allowed to probe t bits of B. We simplify the select index given in [Raman et al., SODA’02] and show how to implement both rank and select queries with an index of size (1 + o(1)) (n lglgn / lgn) + O(n / lgn)(1 + o(1)) (n \lg\lg n / \lg n) + O(n / \lg n) (i.e. we give an explicit constant for storage) in the RAM model with word size lgn\lg n.06/2006: pages 370381; 
Conference Paper: Rank/select operations on large alphabets: a tool for text indexing.
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ABSTRACT: We consider a generalization of the problem of sup porting rank and select queries on binary strings. Given a string of length n from an alphabet of size σ, we give the first representation that supports rank and access operations in O(lg lg σ )t ime, andselect in O(1) time while using the optimal n lg σ + o(n lg σ) bits. The best known previous structure for this prob lem required O(lg σ) time, for general values of σ. Our results immediately improve the search times of a variety of text indexing methods.Proceedings of the Seventeenth Annual ACMSIAM Symposium on Discrete Algorithms, SODA 2006, Miami, Florida, USA, January 2226, 2006; 01/2006 
Conference Paper: Optimal Lower Bounds for Rank and Select Indexes.
Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Venice, Italy, July 1014, 2006, Proceedings, Part I; 01/2006 
Conference Paper: Adaptive Searching in Succinctly Encoded Binary Relations and TreeStructured Documents.
Combinatorial Pattern Matching, 17th Annual Symposium, CPM 2006, Barcelona, Spain, July 57, 2006, Proceedings; 01/2006  [Show abstract] [Hide abstract]
ABSTRACT: In this short note, we improve and extend Yao's paper "On the power of quantum fingerprinting" about simulating a classical public coin simultaneous message protocol by a quantum simultaneous message protocol with no shared resource.11/2005;  [Show abstract] [Hide abstract]
ABSTRACT: Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). Using a variety of benchmark and random problems, we show that on some problems our bounds consistency algorithm can dramatically outperform existing stateoftheart commercial implementations of constraint propagators for the gcc. We also present a new algorithm for domain consistency propagation of the gcc which improves on the worstcase performance of the best previous algorithm for problems that occur often in applications.Constraints 01/2005; 10(2):115135. · 0.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: An optimal broadcasting scheme under the presence of secondary content (i.e. advertisements) is proposed. The proposed scheme works both for movies encoded in a Constant Bit Rate (CBR) or a Variable Bit Rate (VBR) format. It is shown experimentally that secondary content in movies can make VideoonDemand (VoD) broadcasting systems more efficient. An efficient algorithm is given to compute the optimal broadcasting schedule with secondary content, which in particular significantly improves over the best previously known algorithm for computing the optimal broadcasting schedule without secondary content.Proc SPIE 12/2004; 
Conference Paper: Improved Algorithms for the Global Cardinality Constraint.
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ABSTRACT: We study the global cardinality constraint (gcc) and pro pose an O(n1.5d) algorithm for domain consistency and an O(cn + dn) algorithm for range consistency, where n is the number of variables, d the number of values in the domain, and c an output dependent vari able smaller than or equal to n. We show how to prune the cardinality variables in O(n2d + n2.66) steps, detect if gcc is universal in constant time and prove that it is NPHard to maintain domain consistency on extendedGCC.Principles and Practice of Constraint Programming  CP 2004, 10th International Conference, CP 2004, Toronto, Canada, September 27  October 1, 2004, Proceedings; 01/2004  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of finding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an outputsensitive data structure that solves this problem in time for a sequence of n elements. This data structure substantially improves over the naı̈ve generalization of the longest increasing subsequence algorithm and in fact produces an outputsensitive optimal solution.Theoretical Computer Science 01/2004; · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of nding the shortest curve in the plane that has unit width. This problem was rst posed as the iver shore" puzzle by Ogilvy (1972) and is related to the area of online searching. Adhikari and Pitman (1989) proved that the optimal solution has length 2:2782 : : : We present a simpler proof, which exploits the fact that the width of a polygon does not decrease under a certain convexi cation operation.08/2003; 
Conference Paper: Optimal Dynamic VideoonDemand Using Adaptive Broadcasting.
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ABSTRACT: We consider the transmission of a movie over a broadcast network to support several viewers who start watching at arbitrary times, after a wait of at most t wait minutes. A recent approach called harmonic broadcasting optimally solves the case of many viewers watching a movie using a constant amount of bandwidth. We consider the more general setting and v changes dynamically. A natural objective is to minimize the amount of resources required to achieve this task. We introduce two natural measures of resource consumption and performancetotal bandwidth usage and maximum momentary bandwidth usageand propose strategies which are optimal for each of them. In particular, we show that an adaptive form of pyramid broadcasting is optimal for both measures simultaneously, up to constant factors. We also show that the maximum throughput for a fixed network bandwidth cannot be obtained by any online strategy.Algorithms  ESA 2003, 11th Annual European Symposium, Budapest, Hungary, September 1619, 2003, Proceedings; 01/2003 
Conference Paper: the asteroid surveying problem and other puzzles.
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ABSTRACT: We consider two variants of the wellknown "sailor in the fog" puzzle. The first version (the "asteroid surveying" problem) is set in three dimensions and asks for the shortest curve that starts at the origin and intersects all planes at unit distance from the origin. Several possible solutions are suggested in the video, including a curve of length less than 12.08. The second version (the "river shore" problem) asks for the shortest curve in the plane that has unit width. A solution of length 2.2782 is described, which we have proved to be optimal.Proceedings of the 19th ACM Symposium on Computational Geometry, June 810, 2003, San Diego, CA, USA; 01/2003
Publication Stats
354  Citations  
3.90  Total Impact Points  
Top Journals
Institutions

2008–2012

Google Inc.
New York City, New York, United States


2003–2010

University of Waterloo
 David R. Cheriton School of Computer Science
Waterloo, Ontario, Canada


2002

University of New Brunswick
 Faculty of Computer Science
Fredericton, New Brunswick, Canada
