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Questions about ways of storing data so that it can be used advantageously by algorithms.

Worst-case complexity $\boldsymbol{\mathcal{O}(1)}$ insertion $\boldsymbol{\mathcal{O}(log\ \textbf{min}\{w_x, q_x\})}$ get-min, extract-min, delete, and decrease of an element $\boldsymbol{x}$ Where …
answered Jan 5 '13 by A T
In terms of asymptotic space and time complexity, what is the most efficient priority-queue? Specifically I am looking for priority queues which minimize the complexity of inserts, it's ok if deletes …
asked Jul 19 '12 by A T
Worst-case complexity Insert: $\mathcal{O}(1)$ Find-min: $\mathcal{O}(1)$ Decrease-key: $\mathcal{O}(1)$ Delete: $\mathcal{O}(\log \log n)$ Space: $\mathcal{O}(n)$ Proof THEOREM 1. We can implement a …
answered Jul 19 '12 by A T
Worst-case complexity $\mathcal{O}(log\ M)$ insert, search, delete [see 'Lemma 3.1'] $\dagger\ \mathcal{O}(1)$ findMin, findMax, extractMin, extractMax, predecessor, successor $2M + \mathcal{O}(log\ M … answered Jan 4 '13 by A T Finally a simplification of the Brodal queue[1] has been released[2], which unlike[3]; are worst-case values (rather than amortised). Insert:$\mathcal{O}(1)$Find-min:$\mathcal{O}(1)$Decrease:$ …
answered Dec 15 '12 by A T
Worst-case complexity Insert: $\mathcal{O}(1)$ Find-min: $\mathcal{O}(1)$ Decrease-key: $\mathcal{O}(1)$ Delete: $\mathcal{O}(\log \log n)$ Space: $\mathcal{O}(n)$ Proof THEOREM 1. We can implement a …
answered Jan 23 '13 by A T
Find-min in $O(1)$ with expected update time of $O(\sqrt{log\text{ }log\text{ }n})$ See the 2007 paper: Equivalence between priority queues and sorting by Mikkel Thorup. Note: He refers to the 2002 …
answered Apr 17 '12 by A T
Approaching this problem by maintaining two data-structures: an Array and a Binary Tree. To maintain indexing in the array, previously you'd have the $\Omega(\dfrac{\log n}{\log\log n})$ bound; but m …
answered Apr 21 '12 by A T
Analysis Insert: $\mathcal{o}(n\ log\ log\ n)$ Search: $\mathcal{o}(log\ log\ n)$ Delete: $\mathcal{O}(1)$ Space: $\mathcal{O}(n)$ Get-Min: $\mathcal{O}(1)$ Extract-Min: $\mathcal{O}(1)$ Implem …
answered May 19 '12 by A T
Okay, finally got you the complexity you were looking for, and what's best, I found it in the literature: Worst-Case Complexity Delete: $\bf\mathcal{O}(1)$ Delete-min: $\bf\mathcal{O}(1)$ Find-min …
answered Jun 26 '12 by A T
Elements are stored in a single dynamic data-structure $D$ Element ranks are computed by: $\forall i \in n\quad f(i,\ x_i+1) : x_i \in \mathbb{Z^+}$ The function $f$ is weighting based on the value o …
Is there a data structure to maintain an ordered list that supports the following operations in $O(1)$ amortized time? GetElement(k): Return the $k$th element of the list. InsertAfter(x,y): Insert …
Hash table lookup can always be $O(1)$ for static sets, see the 2002 paper by Arne Andersson and Mikkel Thorup: Dynamic ordered sets with exponential search trees Firstly, we give the ﬁrst determi …
Looks like the $\Omega(\dfrac{\log n}{\log\log n})$ barrier has been overcome by modifying the analysis from the chronogram technique. The new [lower] $\Omega(\log n)$ bound has been proved for simil …
How about using a Strict Fibonacci Heap? - Here are the worst-case complexities: $$\mathcal{O}(1) \text{ find-min}$$ $$\mathcal{O}(\log_2 n) \text{ delete-min}$$ $$\mathcal{O}(1) \text{ insert}$$ …