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Dynamic ThreeDimensional Linear Programming
, 1992
"... We perform linear programming optimizations on the intersection of k polyhedra in R³, represented by their outer recursive decompositions, in expected time O(k log k log n + √k log k log³ n). We use this result to derive efficient algorithms for dynamic linear programming ..."
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Cited by 39 (5 self)
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We perform linear programming optimizations on the intersection of k polyhedra in R&sup3;, represented by their outer recursive decompositions, in expected time O(k log k log n + &radic;k log k log&sup3; n). We use this result to derive efficient algorithms for dynamic linear programming problems in which constraints are inserted and deleted, and queries must optimize specified objective functions. As an application, we describe an improved solution to the planar 2center and 2median problems.
Efficient Splitting and Merging Algorithms for Order Decomposable Problems
, 1997
"... Let S be a set whose items are sorted with respect to d ? 1 total orders OE 1 ; : : : ; OE d , and which is subject to dynamic operations, such as insertions of a single item, deletions of a single item, split and concatenate operations performed according to any chosen order OE i (1 i d). This g ..."
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Cited by 15 (2 self)
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Let S be a set whose items are sorted with respect to d ? 1 total orders OE 1 ; : : : ; OE d , and which is subject to dynamic operations, such as insertions of a single item, deletions of a single item, split and concatenate operations performed according to any chosen order OE i (1 i d). This generalizes to dimension d ? 1 the notion of concatenable data structures, such as the 23trees, which support splits and concatenates under a single total order. The main contribution of this paper is a general and novel technique for solving order decomposable problems on S, which yields new and efficient concatenable data structures for dimension d ? 1. By using our technique we maintain S with the following time bounds: O(log n) for the insertion or the deletion of a single item, where n is the number of items currently in S; O(n 1\Gamma1=d ) for splits and concatenates along any order, and for rectangular range queries. The space required is O(n). We provide several applications of ...
A TradeOff For WorstCase Efficient Dictionaries
"... We consider dynamic dictionaries over the universe U = {0, 1}^w on a unitcost RAM with word size w and a standard instruction set, and present a linear space deterministic dictionary accommodating membership queries in time (log log n)^O(1) and updates in time (log n)^O(1), where n is the size of t ..."
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Cited by 7 (2 self)
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We consider dynamic dictionaries over the universe U = {0, 1}^w on a unitcost RAM with word size w and a standard instruction set, and present a linear space deterministic dictionary accommodating membership queries in time (log log n)^O(1) and updates in time (log n)^O(1), where n is the size of the set stored. Previous solutions either had query time (log n) 18 or update time 2 !( p log n) in the worst case.
Deterministic Algorithms for 2d Convex Programming and 3d Online Linear Programming
 3d Online Linear Programming, Journal of Algorithms
, 1997
"... We present a deterministic algorithm for solving twodimensional convex programs with a linear objective function. The algorithm requires O(k log k) primitive operations for k constraints; if a feasible point is given, the bound reduces to O(k log k= log log k). As a consequence, we can decide wheth ..."
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Cited by 7 (3 self)
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We present a deterministic algorithm for solving twodimensional convex programs with a linear objective function. The algorithm requires O(k log k) primitive operations for k constraints; if a feasible point is given, the bound reduces to O(k log k= log log k). As a consequence, we can decide whether k convex ngons in the plane have a common intersection in O(k log nminflogk; log log ng) worstcase time. Furthermore, we can solve the threedimensional online linear programming problem in o(log 3 n) worstcase time per operation. Running Head: 2d Convex Programming 1 Introduction Convex programming in fixeddimensional space is a fundamental problem in computational geometry with many applications. Using randomization, the problem has been solved satisfactorily, as simple methods are known that require only a linear expected number of operations. These methods include a random sampling algorithm by Clarkson [8] and a randomized incremental algorithm by Sharir and Welzl [28]; the...
MultiUser File System Search
, 2007
"... Information retrieval research usually deals with globally visible, static document collections. Practical applications, in contrast, like file system search and enterprise search, have to cope with highly dynamic text collections and have to take into account userspecific access permissions when ..."
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Cited by 5 (1 self)
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Information retrieval research usually deals with globally visible, static document collections. Practical applications, in contrast, like file system search and enterprise search, have to cope with highly dynamic text collections and have to take into account userspecific access permissions when generating the results to a search query. The goal of this thesis is to close the gap between information retrieval research and the requirements exacted by these reallife applications. The algorithms and data structures presented in this thesis can be used to implement a file system search engine that is able to react to changes in the file system by updating its index data in real time. File changes (insertions, deletions, or modifications) are reflected by the search results within a few seconds,
Persistence, Offline Algorithms, and Space Compaction
, 1991
"... We consider dynamic data structures in which updates rebuild a static solution. Space bounds for persistent versions of these structures can often be reduced by using an offline persistent data structure in place of the static solution. We apply this technique to decomposable search problems, to dyn ..."
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We consider dynamic data structures in which updates rebuild a static solution. Space bounds for persistent versions of these structures can often be reduced by using an offline persistent data structure in place of the static solution. We apply this technique to decomposable search problems, to dynamic linear programming, and to maintaining the minimum spanning tree in a dynamic graph. Our algorithms admit tradeoffs of update time vs. query time, and of time vs. space.