
Searching, Sorting, and Cake Cutting in Rounds
We study sorting and searching in rounds motivated by a cake cutting pro...
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Multiparty Selection
Given a sequence A of n numbers and an integer (target) parameter 1≤ i≤ ...
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Optimal Algorithm for Profiling Dynamic Arrays with Finite Values
How can one quickly answer the most and top popular objects at any time,...
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Galloping in natural merge sorts
We study the algorithm TimSort and the subroutine it uses to merge mono...
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Fragile Complexity of ComparisonBased Algorithms
We initiate a study of algorithms with a focus on the computational comp...
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A Class of Optimal Structures for Node Computations in Message Passing Algorithms
Consider the computations at a node in the message passing algorithms. A...
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Chaining with overlaps revisited
Chaining algorithms aim to form a semiglobal alignment of two sequences...
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Fragile Complexity of Adaptive Algorithms
The fragile complexity of a comparisonbased algorithm is f(n) if each input element participates in O(f(n)) comparisons. In this paper, we explore the fragile complexity of algorithms adaptive to various restrictions on the input, i.e., algorithms with a fragile complexity parameterized by a quantity other than the input size n. We show that searching for the predecessor in a sorted array has fragile complexity Θ(log k), where k is the rank of the query element, both in a randomized and a deterministic setting. For predecessor searches, we also show how to optimally reduce the amortized fragile complexity of the elements in the array. We also prove the following results: Selecting the kth smallest element has expected fragile complexity O(loglog k) for the element selected. Deterministically finding the minimum element has fragile complexity Θ(log(Inv)) and Θ(log(Runs)), where Inv is the number of inversions in a sequence and Runs is the number of increasing runs in a sequence. Deterministically finding the median has fragile complexity O(log(Runs) + loglog n) and Θ(log(Inv)). Deterministic sorting has fragile complexity Θ(log(Inv)) but it has fragile complexity Θ(log n) regardless of the number of runs.
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