Using as few resources (e.g. time, space) as possible while solving a problem. Use this tag if your question is specifically about resource usage, not for generic algorithm questions that happen to mention running times.

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22 views

Efficient flood filling (seed filling)

I am referring to the algorithm that fills a white area of arbitrary shape in a binary digital image, starting from a given white pixel, using the Moore (8 neighbors) or Neumann (4 neighbors) ...
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2answers
108 views

Brute force method to solve the 0-1 knapsack problem

I know that the brute force method is not the best way to solve the 0-1 knapsack problem. I'm not quite getting the dynamic programming idea, but would like to know the following: If the brute force ...
7
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1answer
174 views

Given n strings, is one of them a substring of another?

Suppose we are given a collection of $n$ strings, $S_1,\dots,S_n$. I would like to know whether any of those strings is a substring of any other string in the collection. In other words, I'd like an ...
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1answer
23 views

Efficient Array Normalization

I want to normalize elements in an array. The solution I found is to take the sum of the elements and divide each element with this total. Can you find more efficient way of doing this? The runtime I ...
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1answer
120 views

RMQ with $O(\sqrt{n})$ space?

I'm asked to design an RMQ data structure (Range Minimum Query: return index of $min$ in a range $[i,j]$) for an array that has $<=\log(n)$ local minimums (a local minimum is an index $i$ such that ...
2
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1answer
63 views

Finding all partitions of a set s.t. each block contains exactly one subset from a given set of subsets - how hopeless?

Hello and apologies if my question will be too elementary. My background is from arithmetic geometry, but I have been recently faced with certain computational problems of combinatorial nature, where ...
2
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0answers
41 views

Max Flow on low depth DAGs

I have a family of acyclic networks in which every path from the source of a given network to its target has length exactly $3$. I'm aware of a publication that in general, finding a max flow in a DAG ...
5
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1answer
119 views

Are there current benchmarks for algorithms solving Travelling Salesman?

I'm researching the travelling salesman problem and looking for data regarding the current state of affairs regarding solutions and performance. So far the only data I've states that the current ...
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2answers
82 views

Can you explain this improvement to this frequency distribution algorithm?

I came across the following in a text book: Frequency distribution – Given a set of n items, which element occurs the largest number of times in the set? If the items are sorted, we can sweep from ...
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1answer
80 views

Example algorithms for first class in programming for EE students [closed]

I am professor of Electrical Engineering who will teach, for my first time, a class to first-year EE students about programming. This will be their first contact in an academic setting with ...
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2answers
38 views

Greedily Schedule Events based on value/hours

Suppose we are given a list of $n$ events $E = \{E_1, E_2, \ldots, E_n\}$ where each $E_i$ is represented by $(s_i, h_i, v_i)$ or $(start, hours, value)$. So if you attend an entire event that lasts ...
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2answers
99 views

directed graph data structure with fast in/out neighbor query

If I store a directed graph $G$ in adjacency list format, one can find all the out-neighbors $j$ of a given vertex $i$ in $\mathcal O(d)$ time, where $d$ is the max degree of the graph. These are all ...
2
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2answers
76 views

How to filter a very, very large file

I have a very large unsorted file, 1000GB, of ID pairs ID:ABC123 ID:ABC124 ID:ABC123 ID:ABC124 ID:ABC123 ID:ABA122 ID:ABC124 ID:ABC123 ID:ABC124 ID:ABC126 I would like to filter the file for ...
2
votes
1answer
194 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 ...
8
votes
3answers
646 views

When is the AKS primality test actually faster than other tests?

I am trying to get an idea of how the AKS primality test should be interpreted as I learn about it, e.g. a corollary for proving that PRIMES ⊆ P, or an actually practical algorithm for primality ...
2
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1answer
208 views

What is a suitable data structure in this scenario?

I need an efficient data structure for maintaining a set of values. Here, $n_1$ is the number of insertions per unit time; $n_2$ is the number of deletions per unit time; $k$ is the number of searches ...
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1answer
52 views

ARQ Protocols and sequence numbers [closed]

What will happen if sequence number is not used in an ARQ protocol (e.g, Go-back-N, selective repeat)?
6
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1answer
127 views

Why choose D* over Dijkstra?

I understand the basis of A* as being a derivative of Dijkstra, however, I recently found out about D*. From Wikipedia, I can understand the algorithm. What I do not understand is why I would use D* ...
3
votes
2answers
244 views

A heuristic for finding a maximum disjoint set

Background I need to find a largest set of non-overlapping axis-parallel squares, out of a given collection of candidate squares. This problem is NP-complete. Many papers suggest approximation ...
6
votes
2answers
201 views

Looking for a set implementation with small memory footprint

I am looking for implementation of the set data type. That is, we have to maintain a dynamic subset $S$ (of size $n$) from the universe $U = \{0, 1, 2, 3, \dots , u – 1\}$ of size $u$ with ...
1
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1answer
260 views

Efficiently pick a largest set of non-intersecting line segments

Given a set of line segments, how do we identify a subset of maximal cardinality where all line segments are pairwise non-intersecting? Brute force we would get $2^n$ sets to check where $n$ is the ...
2
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0answers
311 views

Choosing the optimal radix/number-of-buckets when sorting n-bit integers using radix sort

This is a popular question: What is the most efficient (in time complexity) way to sort 1 million 32-bit integers? Most answers seem to agree that one of the best ways would be to use radix ...
0
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1answer
102 views

How do context switches factor into CPU utilization?

When studying operation systems, is context switch time included in CPU utilization time? For example, if 5 percent of CPU time is wasted to context switching, is CPU utilization 95 percent?
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3answers
783 views

Which data structure to use for accessing min/max in constant-time?

I need a data structure which can include millions of elements, minimum and maximum must be accesable in constant time and inserting and erasing element time complexity must be better than linear.
2
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0answers
53 views

Calculating the classification threshold efficiently

I have a multi-label classification problem, in which each input sample has a set of zero or more output labels. I have a multi-class classifier which, for every input sample, returns a certain score ...
0
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1answer
825 views

Algorithm to add sum of every possible xor-sum sub-array

I participated in one algorithmic competition. I got stuck in one problem, I am asking the same here. Problem Statement XOR-sum of a sub-array is to XOR all the numbers of that sub-array. An array ...
3
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2answers
134 views

Enumerating weighted permutations in sorted order problem

Let $S$ be a set of $n$ integers. Consider the following weighted permutations problem. Let $m<n$ be an integer. What is an efficient algorithm to enumerate all subsets of $m$ integers of $S$ ...
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2answers
174 views

What do I need to know about algorithms?

Drawing from Are algorithms (and efficiency in general) getting less important?, I get that algorithms are more important than ever, but I need to know anything about them other than their ...
24
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8answers
2k views

Are algorithms (and efficiency in general) getting less important?

Since buying computation power is much affordable than in the past, are the knowledge of algorithms and being efficient getting less important? It's clear that you would want to avoid an infinite ...
13
votes
3answers
7k views

Factorial algorithm more efficient than naive multiplication

I know how to code for factorials using both iterative and recursive (e.g. n * factorial(n-1) for e.g.). I read in a textbook (without been given any further ...
2
votes
1answer
30 views

Finding users covering a set x by x

I have a Set $S$ of objects, a set $U$ of users and a map $c: U \rightarrow S^{\prime}$, where $S^{\prime} \subset S$ and $\emptyset \notin S^{\prime}$. Every time I add a new entry to $c$, i.e. ...
2
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1answer
68 views

Calculate the number of elements after multiplying/adding two polynomials

Suppose I have two polynomials $f(x)$ and $g(x)$ and I somehow represent their coefficients. I have a couple of ways to hold a polynomial depending on how many significant coefficients the polynomial ...
6
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3answers
644 views

What data structure would efficiently store integer ranges?

I need to keep a collection on integers in the range 0 to 65535 so that I can quickly do the following: Insert a new integer Insert a range of contiguous integers Remove an integer Remove all ...
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2answers
149 views

What is the impact of synchronisation overhead on parallel speedup? [closed]

When implementing a parallel version of an algorithm, what is the impact of synchronization delays on speedup efficiency? Does this depend on the platform used? Is coarse-grained parallelism better ...
2
votes
2answers
364 views

What are efficient data structures for inserting and accessing elements?

Is there a data structure to keep a list of elements (not necessarily sorted) that performs the Access (by index) and Insert operations in a reasonable asymptotic time? When I say "reasonable time", ...
2
votes
3answers
793 views

What is the most power/energy efficient sorting algorithm?

I am writing a Android phone application that needs to be very power efficient, and I would like to use the most power efficient sorting algorithm. I will implement it in C for extra power efficiency. ...
7
votes
3answers
10k views

Why is selection sort faster than bubble sort?

It is written on Wikipedia that "... selection sort almost always outperforms bubble sort and gnome sort." Can anybody please explain to me why is selection sort considered faster than bubble sort ...
6
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1answer
164 views

Largest reported speedup for a parallel computation?

A parallel implementation of a computation is usually compared to a sequential version of the same computation. The ratio of the time taken by the sequential version to the time taken by the parallel ...
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3answers
186 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 ...
1
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4answers
963 views

What are flops and how are they benchmarked?

Apple has just proudly stated that their new mac pro will be able to give up to 7 teraflops of computing power. Flops stands for Floating Point Operations Per Second. How exactly is this benchmarked ...
2
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0answers
194 views

Why does Shellsort work well on Sorted and Reverse ordered lists?

I've ran some tests and found that Shellsort runs much faster on ordered and reversed lists compared to random lists and almost ordered lists. ...
4
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3answers
2k views

Explaining why FFT is faster than DFT for the general public?

How would you explain why the Fast Fourier Transform is faster than the Discrete Fourier Transform, if you had to give a presentation about it for the general (non-mathematical) public?
6
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1answer
106 views

Relaxed Bin Packing Problem

The problem I have is like this bin packing problem, but instead I have $n$ bins and a collection of items with discrete masses. I need to put at least $m$ kg of stuff in each bin. Is there an ...
2
votes
1answer
133 views

Optimized algorithm to compare templates of two websites

My task is to compare templates of two websites. I am ready with my algorithm. But it takes too much time to give a final answer. Here, "template" means the way any page presents its contents. ...
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2answers
225 views

How do we determine how much time a multi-tape DTM saves over a one-tape DTM?

Note: This is a part of a homework question Were asked to construct a multi-tape Turing Machine for language {$a^n b^n c^n \mid n \geq 0$} Then it says "Discuss how much time your machines saves ...
2
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1answer
128 views

Are genetic algorithms special instances of random search done in an unexpectedly short run-time? [closed]

I was wondering since randomness is embedded in genetic algorithms at almost every level, is there a really fine line between genetic algorithms and pure random search? Ever since I finished my ...
1
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1answer
50 views

Random file access in a block based file format

I am writing a program to store, retrieve and delete "blocks" of data of varying sizes. The way it currently works is by keeping a database storing the locations of the blocks and the locations of ...
1
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1answer
589 views

Complexity of algorithm inserting an element in a circular linked list at the front end

In a circular linked list, if an elements needs to be inserted at front [just before the node pointed by head], can be done in O(1) (see the answer here) But in a book currently, I have, it is ...
5
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1answer
104 views

A vector-like data structure with allocation table; O(1) indexing time required

I am a beginner in data structures and recently came across a vector implemented on an array, which is extended on demand. Of course the table cannot be extended "in place", we must allocate a new ...
2
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4answers
289 views

Speeding up a program solving Icosoku

I bought a great puzzle called Icosoku. Wikipedia describes it as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and ...