Publications (27)8.13 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. 
Conference Paper: On the complexity of routing in wireless multihop network
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ABSTRACT: Wireless backbone networks represent an attractive alternative to wired networks in situations where cost, speed of deployment, and flexibility in network design are important. In typical configurations, users connect to wireless routers of the backbone network, which then redirect the traffic to one of the existing network gateways. To improve the network performance, wireless backbone routers redirect their traffic to the network gateways so as to maximize amount of traffic that can be supported by the network. In this paper, we prove that this problem is NPhard as a result of the wireless interference that is created between geographically close transmission links. We consequently design and investigate the performance of interferenceaware algorithms suitable for multichannel environments against more traditional routing approaches. We evaluate their performance in simulated environments based on data taken from existing networks, and show that interferencebased heuristics exhibit advantageous performance in nonuniform deployment.  [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).  [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. 
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. 
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. 
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. 
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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 trees  [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. 
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. 

Conference Paper: Optimal Lower Bounds for Rank and Select Indexes.
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ABSTRACT: We develop a new lower bound technique for data structures. We show an optimal Q (n Ig Ig n/ Ig 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 Omega((m/t) Ig 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 Ig Ig n/ Ig n) + O(n/ Ig n) (i.e. we give an explicit constant for storage) in the RAM model with word size Ig n.  [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.  [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.  [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. 
Conference Paper: Improved Algorithms for the Global Cardinality Constraint
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ABSTRACT: We study the global cardinality constraint (gcc) and propose an O(n 1.5d) 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 variable smaller than or equal to n. We show how to prune the cardinality variables in O(n 2d + n 2.66) steps, detect if gcc is universal in constant time and prove that it is NPHard to maintain domain consistency on extendedGCC.  [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.  [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. 
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.
Publication Stats
458  Citations  
8.13  Total Impact Points  
Top Journals
Institutions

20082012

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


20032010

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