Questions tagged [priority-queues]
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52
questions
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How to compute the general term formula for the number of full binary tree heaps that can be formed with distinct elements?
The number of possible heaps that are full binary trees of height $h$ and can be formed with ($n = 2^h - 1$) distinct elements can be computed by recursion:
$$ a_h = {2^h - 2 \choose 2^{h - 1} - 1} a_{...
2
votes
1answer
80 views
Dijkstra without decrease key
I was reading though this paper,
which suggests using dijkstra without
edge relaxation, but to rather to just insert new nodes, cf page 16 for the pseudo code. But to me the code looks wrong. I think ...
3
votes
0answers
111 views
Making an array increasing by modifying elements
I am trying to solve a problem on codeforces. Given an integer array $a_1,\ldots,a_n$, our goal is to find the minimal number of instructions, each of which increments or decrements a single entry, ...
2
votes
2answers
58 views
Why can't we replace Dijkstra's priority queue with a regular queue?
I am confused why we can't simply use a normal queue instead of a priority queue for Dijkstra's. I agree that you can find the shortest path in fewer iterations of the while loop using a priority ...
2
votes
1answer
24 views
Parallelization of priority queue-based algorithms
There's a number of algorithms that operate by maintaining and consuming a priority queue of "events". I'm thinking primarily of geometric algorithms, particularly sweep-line algorithms like Bentley-...
0
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0answers
25 views
When inserting an element in a priority queue and the heap size is already at max capacity, should you output an error OR increase the array size?
I'm currently learning about how to implement priority queues using heaps, but I've hit a wall while trying to implement the insertion operation. Assume that the size of the array storing the ...
1
vote
1answer
42 views
Priority queue with a buffer for delayed insertion and other tweaks
I was thinking of ways to optimise a (heap-based) priority queue in certain scenarios, like in best-first path search algorithms (Dijkstra, A*, etc.).
One possible optimisation is to delay insertions ...
0
votes
1answer
57 views
Short Fibonacci Heap
Is it possible to create a Fibonacci Heap that has exactly 5 nodes: one root node and 4 children of that root?. If yes please explain the sequence of operations to do so. If it is not possible then ...
1
vote
1answer
48 views
An algorithm to drop low-priority items from a heap-based priority queue
I am looking for an efficient algorithm to drop from a complete binary min heap all items whose weight exceeds a given value. (Or, equivalently, to drop from a priority queue realised by such a heap ...
1
vote
1answer
47 views
Heap operating in time $\Gamma^{-1}(n)^2$
I have a priority queue implementation which I claim has the following worst case asymptotic run-times for the given operations:
PEEK_MIN …………………………… O(1)
POP_MIN…………………………… O( (INVERSE_Γ(n)) ^2).
...
1
vote
2answers
349 views
Is there a name for this priority queue data structure?
While watching a sports tournament, I noticed that the tournament tree looks a lot like a heap. I came up with the following data structure: A complete binary tree where the leaves are elements of ...
0
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1answer
389 views
Why is a heap better than a linked list for implementation of a priority queue?
Using a heap, you have O(log(n)) insertion and O(log(n)) removal. Using a linked list, you have O(n) insertion and O(1) removal.
Why is it better to have log-n for both than n for one and constant ...
1
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0answers
40 views
How priority queue is used in Dijsktra algorithm?
I have difficulties understanding how the priority queue is used in Dijkstra algorithm. Wikipedia lists 3 operations performed on priority queue:
add_with_priority(),
extract_min(),
...
1
vote
2answers
80 views
Sorting in a Priority Queue
Does a priority queue Queue<K,V> always sort its elements based on the value of each element or its key?
I know than the priority in the queue is based on ...
1
vote
1answer
43 views
Complexity of closest set of points in plane problem
Given a set of points on a plane find the set of $n$ points that are closest to the origin. (Points are pairs of integers.)
Input: list of points.
Initialize a priority queue $Q$, where ...
1
vote
2answers
64 views
Priority queue of constant size fit for extraction of K highest priority elements
In an algorithm I'm designing, I need to do this cycle on a priority queue of constant size N many times, as quickly as possible:
get $K$ highest priority elements (do on them some outside ...
2
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0answers
394 views
How would a priority queue be implemented in a functional programming language?
How would a priority queue be coded efficiently in a functional programming language? I'm new to functional programming, but I'm having difficulty understanding how a data structure that seems to ...
1
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2answers
266 views
Correct term for a priority queue with unique elements
Is there a standard term for a priority queue which can only hold a single occurrence of any element? This would be a priority queue for which operations such as "raise the priority of element ...
1
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1answer
138 views
Leftist Tree initialization in O(n) time
In the book Handbook of Data Structures and Applications, section 5.2.5, (copy of the relevant section available here) about leftist queues, the author(s) state the following:
For the complexity ...
0
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0answers
1k views
Find K largest elements using a priority queue [duplicate]
Say we have a Priority Queue of size 1000 that is implemented using Max Heap.
Now if i want to get the top 5 elements, the most laid back method is to poll the maximum 5 times, resulting in a set of ...
0
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1answer
262 views
Bucket Priority Queues with large integers for $O(1)$ insert and extract~min?
I recently got into a discussion about Priority Queues when the requirements allow for "best effort" removal (i.e. the removed key may not always be THE very highest priority, but it is relatively ...
0
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2answers
66 views
Why do we need increase_key procedure in max priority queue?
Since if I want to increase the priority of a specific node, how do I find the node without linear searching it.
I need to pass the index to this function, which is in a way a bottleneck. So the ...
4
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2answers
178 views
Devise algorithm to travel destinations in a way that you always have enough money for the next destination (getting paid at each destination as well)
This problem probably falls under some category of algorithms but I don't know which.
A given restaurant has $b_1..b_n$ branches around the world. A food critic has to travel all of the branches.
...
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0answers
2k views
Bubble down implementation for min-heap
While going through bubble_down implementation for min-heap in The Algorithm Design Manual By Steven Skiena, since routine ...
1
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2answers
638 views
How to classify simple priority queue algorithm
I have a simple priority queue algorithm that I implemented, and I doubt it's new
but I haven't been able to classify it. Wondering if I could get some help with classifying it! Once I classify it I ...
2
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0answers
331 views
Unique integer priority queue with both $O(1)$ insert and extract-min?
I'm aware of the two questions prioritizing inserts and extracts individually, each in $O(1)$ time, but does there exist a unique integer priority queue algorithm for the range $[0, n)$ that can do ...
6
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1answer
361 views
Best data structure for a queue with random reads?
Well, it's not exactly a queue if it allows for random reads. This question is about a data structure which behaves like a queue for insertions and a sorted dictionary for reads.
Imagine an algorithm ...
2
votes
1answer
54 views
Efficient haircuts
I have a real vector $v$. From this vector, I want to extract a sequence of integers, $ix$. The first integer is found by, $ix_0=argmax(v)$. 1 is then subtracted from $v_{ix_0}$, and the process is ...
2
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2answers
6k views
Finding the median in a heap
Given a binary heap $H$, indexed in $[1..n]$, whose elements are integers, is there a way to quickly find its median in $O(\log n)$-time?
7
votes
1answer
6k views
Why in a min priority queue (heap based) it is called “decrease-key” and not just “set-key”?
When you call decrease-key in a min priority queue, you are basically setting the key, you can accidentally put a higher key, right? so why isn't it called "set-key" or "update-key"? why (according to ...
5
votes
1answer
675 views
Heap-like data structure allowing peek at largest & smallest
For the purpose of implementing an optimization algorithm (finding the minimum of a multivariate function) I want to create a data structure that supports the following operations:
load from array
...
0
votes
2answers
7k views
How to calculate probability of packet loss and drop rate?
In a queuing system (M/M/1) with a finite packet capacity $z$, how do you determine the probability of packet loss if we assume that packets are dropped when the system is full? Packets arrive with a ...
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0answers
3k views
Where To Put Duplicates in Max Heap?
Question:
Suppose you have a list of integers and it might contain duplicates. Build a Max Heap using this list. Where would the duplicates of the max integer reside in this Max Heap data structure?...
0
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1answer
90 views
What will trigger a worst time search for a binary heap and what is the run time? [closed]
I thought if the values in a max or min heap is monotonically increasing or decreasing, then this will trigger a worst case run time of $\mathcal{O}(n)$ because you will have to go through each and ...
0
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0answers
724 views
Dynamically weighted priority queue?
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 of ...
4
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0answers
261 views
Concurrent priority queue with lazy increase-key
I could use a priority queue supporting the find-and-delete-min, and lazy-increase-key operations. The last term is my "...
3
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1answer
553 views
Can we create binomial heaps in linear time?
I'm studying binomial heaps in anticipation for my finals and the CLRS book tells me that insertion in a binomial heap takes $\Theta(\log n)$ time. So given an array of numbers it would take $\Theta(n\...
1
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2answers
111 views
“Minimum Stack”
I am now preparing for a test in my algorithms course and I have stumbled upon a question about a data structure which seems too trivial for me, but is probably not trivial at all.
The question is:
...
3
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2answers
2k views
Priority queue with unique elements and sublinear time merge?
Some priority queues, like the height-based leftist tree (or here) support merging in $\mathcal O\left(\log n\right)$ time.
I am looking for a priority queue that merges in (expected|average|...
1
vote
1answer
911 views
Which priority queue implementations are stable?
I can't answer this question. It seems simple but I really don't know how to approach it.
Here it is:
A priority queue is said to be stable if deletions of items with equal priority value occur in ...
15
votes
2answers
29k views
Heap - Give an $O(n \lg k)$ time algorithm to merge $k$ sorted lists into one sorted list
Most probably, this question is asked before. It's from CLRS (2nd Ed) problem 6.5-8 --
Give an $O(n \lg k)$ time algorithm to merge $k$ sorted lists into one sorted list, where $n$ is the total ...
1
vote
3answers
642 views
Priority queue with ubounded number of elements (i.e., with dynamic storage)
I'm looking for a data structure that can work as a priority queue with reasonable maintenance complexities (like $O(\log n)$ for insertion and deletion) and that has a theoretical unbounded limit for ...
2
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1answer
1k views
Load balancing. Why not use priority queues?
I have recently learned about various randomized algorithms for load balancing. The model is always that there are $m$ balls and $n$ bins and the balls arrive one at a time. The task is to minimize ...
2
votes
1answer
88 views
performance between the data structures
I have developed two existing data structures and I want to see their performances over a certain algorithm. In this case I use Dijkstra's algorithm with binary and Fibonacci heaps. Just to ask, if I ...
16
votes
3answers
37k views
Increase-key and decrease-key in a binary min-heap
In many discussions of binary heap, normally only decrease-key is listed as supported operation for a min-heap. For example, CLR chapter 6.1 and this wikipedia page. Why isn't increase key normally ...
16
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6answers
1k views
Priority queue for partially ordered priorities with infima
I have a some objects with priority that is compound type and is only partially ordered. I need to select the objects in order of this priority (i.e. yield minimal item each time). But rather than ...
5
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2answers
2k views
Lower bounds: queues that return their min elements in $O(1)$ time
First, consider this simple problem --- design a data structure of comparable elements that behaves just like a stack (in particular, push(), pop() and top() take constant time), but can also return ...
4
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1answer
427 views
Batch processing in increase-key function using binary heap
Is there an algorithm to perform batch processing in the increase-key operation? Let us say, a binary heap (min-heap) is used. In the normal increase-key function, if we perform increase key on one ...
2
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5answers
7k views
Most efficient known priority queue for inserts
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 ...
3
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1answer
2k views
Queue that can sort by multiple priorities?
I have a high interest in priority-queues (E.g., see my answers on: Does there exist a priority queue with $O(1)$ extracts?), and was wondering if there is a priority-queue or similar data-structure ...
