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Data Structural Bootstrapping, Linear Path Compression, and Catenable Heap Ordered Double Ended Queues
 SIAM Journal on Computing
, 1992
"... A deque with heap order is a linear list of elements with realvalued keys which allows insertions and deletions of elements at both ends of the list. It also allows the findmin (equivalently findmax) operation, which returns the element of least (greatest) key, but it does not allow a general delet ..."
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A deque with heap order is a linear list of elements with realvalued keys which allows insertions and deletions of elements at both ends of the list. It also allows the findmin (equivalently findmax) operation, which returns the element of least (greatest) key, but it does not allow a general deletemin (deletemax) operation. Such a data structure is also called a mindeque (maxdeque) . Whereas implementing mindeques in constant time per operation is a solved problem, catenating mindeques in sublogarithmic time has until now remained open. This paper provides an efficient implementation of catenable mindeques, yielding constant amortized time per operation. The important algorithmic technique employed is an idea which is best described as data structural bootstrapping: We abstract mindeques so that their elements represent other mindeques, effecting catenation while preserving heap order. The efficiency of the resulting data structure depends upon the complexity of a special case of pa...
New Applications of Failure Functions
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1987
"... Several algorithms are presented whose operations are governed by a principle of failure functions: when searching for an extremal value within a sequence, it suffices to consider only the subsequence of items each of which is the first possible improvement of its predecessor. These algorithms are m ..."
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Cited by 4 (0 self)
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Several algorithms are presented whose operations are governed by a principle of failure functions: when searching for an extremal value within a sequence, it suffices to consider only the subsequence of items each of which is the first possible improvement of its predecessor. These algorithms are more efficient than their more traditional counterparts.
The Traveler’s Problem
"... The Traveler’s Problem (TP) entails determining the maximum distance that can be traversed along a road, given the locations and room rates of inns along that road, and given the constraints of maximum distance per day and limited budget available for overnight stays at ..."
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The Traveler’s Problem (TP) entails determining the maximum distance that can be traversed along a road, given the locations and room rates of inns along that road, and given the constraints of maximum distance per day and limited budget available for overnight stays at
Partitioning Number Sequences into Optimal Subsequences
"... We consider how to partition finite sequences of positive numbers into subsequences such that each resulting subsequence has a sum of at least a given minimum. Given several di#erent optimality criteria, based on maximising the number of subsequences and minimising their variance in size, we develop ..."
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We consider how to partition finite sequences of positive numbers into subsequences such that each resulting subsequence has a sum of at least a given minimum. Given several di#erent optimality criteria, based on maximising the number of subsequences and minimising their variance in size, we develop and analyse a series of algorithms that yield optimal solutions.
Performance guarantees for Btrees . . .
, 2010
"... Most Btree papers assume that all N keys have the same size K, that f = B/K keys fit in a disk block, and therefore that the search cost is O(log f+1 N) block transfers. When keys have variable size, however, Btree operations have no nontrivial performance guarantees. This paper provides Btreeli ..."
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Most Btree papers assume that all N keys have the same size K, that f = B/K keys fit in a disk block, and therefore that the search cost is O(log f+1 N) block transfers. When keys have variable size, however, Btree operations have no nontrivial performance guarantees. This paper provides Btreelike performance guarantees on dictionaries that contain keys of different sizes in a model in which keys must be stored and compared as opaque objects. The resulting atomickey dictionaries exhibit performance bounds in terms of the average key size and match the bounds when all keys are the same size. Atomic key dictionaries can be built with minimal modification to the Btree structure, simply by choosing the pivot keys properly. This paper describes both static and dynamic atomickey dictionaries. In the static case, if there are N keys with average size K, the search cost is O(⌈K/B ⌉ log 1+⌈B/K ⌉ N) expected transfers. The paper proves that it is not possible to transform these expected bounds into worstcase bounds. The cost to build the tree is O(NK) operations and O(NK/B) transfers if all keys are presented in sorted order. If not, the cost is the sorting cost. For the dynamic dictionaries, the amortized cost to insert a key κ of arbitrary length at an arbitrary rank is dominated by the cost to search for κ. Specifically the amortized cost to insert a key κ of arbitrary length and random rank is O(⌈K/B ⌉ log 1+⌈B/K ⌉ N + κ  /B) transfers. A dynamicprogramming algorithm is shown for constructing a search tree with minimal expected cost.