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33
Fast fractional cascading and its applications
, 2003
"... Using the notions of Qheaps and fusion trees developed by Fredman and Willard, we develop a faster version of the fractional cascading technique while maintaining the linear space structure. The new version enables sublogarithmic iterative search in the case when we have a search tree and the degre ..."
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Using the notions of Qheaps and fusion trees developed by Fredman and Willard, we develop a faster version of the fractional cascading technique while maintaining the linear space structure. The new version enables sublogarithmic iterative search in the case when we have a search tree and the degree of each node is bounded by O(log n), for some constant> 0, where n is the total size of all the lists stored in the tree. The fast fractional cascading technique is used in combination with other techniques to derive sublogarithmic time algorithms for the geometric retrieval problems: orthogonal segment intersection and rectangular point enclosure. The new algorithms use O(n) space and achieve a query time of O(log n = log log n + f), where f is the number of objects satisfying the query. All our algorithms assume the version of the RAM model used by Fredman and Willard. 1
Hashing, Randomness and Dictionaries
, 2002
"... This thesis is centered around one of the most basic information retrieval problems, namely that of storing and accessing the elements of a set. Each element in the set has some associated information that is returned along with it. The problem is referred to as the dictionary problem, due to the si ..."
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This thesis is centered around one of the most basic information retrieval problems, namely that of storing and accessing the elements of a set. Each element in the set has some associated information that is returned along with it. The problem is referred to as the dictionary problem, due to the similarity to a bookshelf dictionary, which contains a set of words and has an explanation associated with each word. In the static version of the problem the set is fixed, whereas in the dynamic version, insertions and deletions of elements are possible. The approach
A new framework for addressing temporal range queries and some preliminary results
, 2003
"... Given a set of n objects, each characterized by d attributes speci ed at m xed time instances, we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently. Whenm =1, our problem reduces to the ddimensiona ..."
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Given a set of n objects, each characterized by d attributes speci ed at m xed time instances, we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently. Whenm =1, our problem reduces to the ddimensional orthogonal search problem. We establish e cient data structures to handle several classes of the general problem. Our results include a linear size data structure that enables a query time of O(log n log m = log log n + f) for onesided queries when d = 1, where f is the number of objects satisfying the query. A similar result is shown for counting queries. We alsoshow that the most general problem can be solved with a polylogarithmic query time using nonlinear space data structures. 1
Onlinemin: A fast strongly competitive randomized paging algorithm
 In In Proc. 9th Workshop on Approximation and Online Algorithms
, 2011
"... Abstract. In the field of online algorithms paging is one of the most studied problems. For randomized paging algorithms a tight bound of Hk on the competitive ratio has been known for decades, yet existing algorithms matching this bound have high running times. We present the first randomized pagin ..."
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Abstract. In the field of online algorithms paging is one of the most studied problems. For randomized paging algorithms a tight bound of Hk on the competitive ratio has been known for decades, yet existing algorithms matching this bound have high running times. We present the first randomized paging approach that both has optimal competitiveness and selects victim pages in subquadratic time. In fact, if k pages fit in internal memory the best previous solution required O(k 2) time per request and O(k) space, whereas our approach takes also O(k) space, but only O(log k) time in the worst case per page request. 1
Dynamic integer sets with optimal rank, select, and predecessor search. arXiv preprint arXiv:1408.3045
, 2014
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S.: Single and multiple consecutive permutation motif search
 Algorithms and Computation, Lecture Notes in Computer Science
, 2013
"... Abstract. Let t be a permutation (that shall play the role of the text) on [n] and a pattern p be a sequence of m distinct integer(s) of [n], m ≤ n. The pattern p occurs in t in position i if and only if p1... pm is orderisomorphic to ti... ti+m−1, that is, for all 1 ≤ k < ` ≤ m, pk> p ` if ..."
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Abstract. Let t be a permutation (that shall play the role of the text) on [n] and a pattern p be a sequence of m distinct integer(s) of [n], m ≤ n. The pattern p occurs in t in position i if and only if p1... pm is orderisomorphic to ti... ti+m−1, that is, for all 1 ≤ k < ` ≤ m, pk> p ` if and only if ti+k−1> ti+`−1. Searching for a pattern p in a text t consists in identifying all occurrences of p in t. We first present a forward automaton which allows us to search for p in t in O(m2 log logm + n) time. We then introduce a MorrisPratt automaton representation of the forward automaton which allows us to reduce this complexity to O(m log logm+ n) at the price of an additional amortized constant term by integer of the text. Both automata occupy O(m) space. We then extend the problem to search for a set of patterns and exhibit a specific AhoCorasick like algorithm. Next we present a sublinear average case search algorithm running in O m logm log logm + n logm m log logm time, that we eventually prove to be optimal on average. 1
Dynamic 3sided Planar Range Queries with Expected Doubly Logarithmic Time
 Proceedings of ISAAC, 2009
"... Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their xcoordinates drawn from a class of smooth distributions, whereas the ycoordinates are arbitrarily distr ..."
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Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their xcoordinates drawn from a class of smooth distributions, whereas the ycoordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(log log n + t) expected time with high probability and updates in O(log log n) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(log log B n + t/B) expected I/Os with high probability and updates in O(log B log n) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution. 1
Efficient IP table lookup via adaptive stratified trees with selective reconstructions
 12TH EUROPEAN SYMP ON ALGORITHMS
, 2004
"... IP address lookup is a critical operation for high bandwidth routers in packet switching networks such as Internet. The lookup is a nontrivial operation since it requires searching for the longest prefix, among those stored in a (large) given table, matching the IP address. Ever increasing routing ..."
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IP address lookup is a critical operation for high bandwidth routers in packet switching networks such as Internet. The lookup is a nontrivial operation since it requires searching for the longest prefix, among those stored in a (large) given table, matching the IP address. Ever increasing routing tables size, traffic volume and links speed demand new and more efficient algorithms. Moreover, the imminent move to IPv6 128bit addresses will soon require a rethinking of previous technical choices. This article describes a the new data structure for solving the IP table look up problem christened the Adaptive Stratified Tree (AST). The proposed solution is based on casting the problem in geometric terms and on repeated application of efficient local geometric optimization routines. Experiments with this approach have shown that in terms of storage, query time and update time the AST is at a par with state of the art algorithms based on data compression or string manipulations (and often it is better on some of the measured quantities).
CacheOblivious Dictionaries and Multimaps with Negligible Failure Probability
"... A dictionary (or map) is a keyvalue store that requires all keys be unique, and a multimap is a keyvalue store that allows for multiple values to be associated with the same key. We design hashingbased indexing schemes for dictionaries and multimaps that achieve worstcase optimal performance for ..."
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A dictionary (or map) is a keyvalue store that requires all keys be unique, and a multimap is a keyvalue store that allows for multiple values to be associated with the same key. We design hashingbased indexing schemes for dictionaries and multimaps that achieve worstcase optimal performance for lookups and updates, with minimal space overhead and subpolynomial probability that the data structure will require a rehash operation. Our dictionary structure is designed for the Random Access Machine (RAM) model, while our multimap implementation is designed for the cacheoblivious external memory (I/O) model. The failure probabilities for our structures are subpolynomial, which can be useful in cryptographic or dataintensive applications.
Dynamic Interpolation Search Revisited
"... A new dynamic Interpolation Search (IS) data structure is presented that achieves O(log log n) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previou ..."
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A new dynamic Interpolation Search (IS) data structure is presented that achieves O(log log n) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previous result holds for IS when the probability of key collisions is measurable. Moreover, our data structure exhibits O(1) expected search time with high probability for a wide class of input distributions that contains all those for which o(log log n) expected search time was previously known.