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Active Learning on Trees and Graphs
"... We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the nonqueried ..."
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Cited by 9 (1 self)
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We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the nonqueried nodes. Our query selection algorithm is extremely efficient, and the optimal number of mistakes on the nonqueried nodes is achieved by a simple and efficient mincut classifier. Through asimplemodificationofthequeryselectionalgorithmwealsoshowoptimality(uptoconstant factors) with respect to the tradeoff between number of queries and number of mistakes on nonqueried nodes. By using spanning trees, our algorithms can beefficientlyappliedtogeneralgraphs, although the problem of finding optimal and efficient active learning algorithms for general graphs remains open. Towards this end, we provide a lower bound on the numberofmistakesmade on arbitrary graphs by any active learning algorithm using a number of queries which is up to a constant fraction of the graph size. 1
A framework for speeding up priorityqueue operations
, 2004
"... Abstract. We introduce a framework for reducing the number of element comparisons performed in priorityqueue operations. In particular, we give a priority queue which guarantees the worstcase cost of O(1) per minimum finding and insertion, and the worstcase cost of O(log n) with at most log n + O ..."
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Cited by 8 (8 self)
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Abstract. We introduce a framework for reducing the number of element comparisons performed in priorityqueue operations. In particular, we give a priority queue which guarantees the worstcase cost of O(1) per minimum finding and insertion, and the worstcase cost of O(log n) with at most log n + O(1) element comparisons per minimum deletion and deletion, improving the bound of 2log n + O(1) on the number of element comparisons known for binomial queues. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and log n equals max {1,log 2 n}. We also give a priority queue that provides, in addition to the abovementioned methods, the prioritydecrease (or decreasekey) method. This priority queue achieves the worstcase cost of O(1) per minimum finding, insertion, and priority decrease; and the worstcase cost of O(log n) with at most log n + O(log log n) element comparisons per minimum deletion and deletion. CR Classification. E.1 [Data Structures]: Lists, stacks, and queues; E.2 [Data
Two new methods for transforming priority queues into doubleended priority queues
 CPH STL Report
, 2006
"... Abstract. Two new ways of transforming a priority queue into a doubleended priority queue are introduced. These methods can be used to improve all known bounds for the comparison complexity of doubleended priorityqueue operations. Using an efficient priority queue, the first transformation can pr ..."
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Cited by 5 (5 self)
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Abstract. Two new ways of transforming a priority queue into a doubleended priority queue are introduced. These methods can be used to improve all known bounds for the comparison complexity of doubleended priorityqueue operations. Using an efficient priority queue, the first transformation can produce a doubleended priority queue which guarantees the worstcase cost of O(1) for findmin, findmax, and insert; and the worstcase cost of O(lg n) including at most lg n + O(1) element comparisons for delete, but the data structure cannot support meld efficiently. Using a meldable priority queue that supports decrease efficiently, the second transformation can produce a meldable doubleended priority queue which guarantees the worstcase cost of O(1) for findmin, findmax, and insert; the worstcase cost of O(lg n) including at most lg n + O(lg lg n) element comparisons for delete; and the worstcase cost of O(min {lg m, lg n}) for meld. Here, m and n denote the number of elements stored in the data structures prior to the operation in question, and lg n is a shorthand for log 2 (max {2, n}). 1.
An experimental evaluation of navigation piles
, 2006
"... Abstract. A navigation pile, which can be used as a priority queue, is an extension of a selection tree. In a compact form the whole data structure requires only a linear number of bits in addition to the elements stored. In this paper, we study the practical efficiency of three different implementa ..."
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Cited by 2 (2 self)
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Abstract. A navigation pile, which can be used as a priority queue, is an extension of a selection tree. In a compact form the whole data structure requires only a linear number of bits in addition to the elements stored. In this paper, we study the practical efficiency of three different implementations of navigation piles and compare their efficiency against two implementations of binary heaps. The results of our experiments show that navigation piles are a good alternative to heaps when element moves are expensive—even if heaps store pointers to elements instead of elements. Based on the experimental comparison of the three navigationpile implementations it is clear that care should be taken when applying space saving strategies that increase the number of instructions performed. In addition to our experimental findings, we give a new and simple way of dynamizing a static navigation pile. Furthermore, we introduce a pointerbased navigation pile which is inherently dynamic in its nature and can be made to support deletions as well. 1.
Priority Queues and Sorting for ReadOnly Data
"... Abstract. We revisit the randomaccessmachine model in which the input is given on a readonly randomaccess media, the output is to be produced to a writeonly sequentialaccess media, and in addition there is a limited randomaccess workspace. The length of the input is N elements, the length of ..."
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Cited by 1 (0 self)
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Abstract. We revisit the randomaccessmachine model in which the input is given on a readonly randomaccess media, the output is to be produced to a writeonly sequentialaccess media, and in addition there is a limited randomaccess workspace. The length of the input is N elements, the length of the output is limited by the computation itself, and the capacity of the workspace is O(S + w) bits,whereS is a parameter specified by the user and w is the number of bits per machine word. We present a stateoftheart priority queue—called an adjustable navigation pile—for this model. Under some reasonable assumptions, our priority queue supports minimum and insert in O(1) worstcase time and extract in O(N/S +lgS) worstcase time, where lg N ≤ S ≤ N / lg N. We also show how to use this data structure to simplify the existing optimal O(N 2 /S + N lg S)time sorting algorithm for this model. 1