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4
votes
1answer
122 views

Finding an element in a sorted array with at most three queries to larger elements

Given a sorted array A, we have to find the position of an element m in it. (It is also given that the element exists in the array.) However there is a constraint. Like in a game you have 3 lives. If ...
1
vote
1answer
51 views

How to synchronize a 2d cellular automaton in $\Theta(\sqrt{n} \log n)$ steps

Let's assume we have given a two dimensional cellular automaton with an initial configuration where alls cells are in an quiescent state, expect for one square of cells. Let $n$ be the number of cells ...
5
votes
2answers
175 views

Decomposing an Algorithm into Local Transformations/Perturbations

Is it common to try to improve an algorithm by decomposing its action on a topological piece of data (e.g. graphs, geometric data) into a series of steps, each of which only makes a local ...
4
votes
1answer
262 views

How partitioning in map-reduce work?

Assume a map-reduce program has $m$ mappers and $n$ reducers ($m > n$). The output of each mapper is partitioned according to the key value and all records having the same key value go into the ...
40
votes
4answers
12k views

What is the novelty in MapReduce?

A few years ago, MapReduce was hailed as revolution of distributed programming. There have also been critics but by and large there was an enthusiastic hype. It even got patented! [1] The name is ...
3
votes
1answer
107 views

Can bottom-up architectures be effectively programmed in top-down paradigms?

The subsumption architecture, proposed by Rodney Brooks in 1986, is a "bottom-up" approach, in which robots are designed using simple hierarchical models. These models build upon and subsume the ...
9
votes
2answers
2k views

When can I use dynamic programming to reduce the time complexity of my recursive algorithm?

Dynamic programming can reduce the time needed to perform a recursive algorithm. I know that dynamic programming can help reduce the time complexity of algorithms. Are the general conditions such that ...
10
votes
1answer
205 views

Preprocess an array for counting an element in a slice (reduction to RMQ?)

Given an array $a_1,\ldots,a_n$ of natural numbers $\leq k$, where $k$ is a constant, I want to answer in $O(1)$ queries of the form: "how many times does $m$ appear in the array between indices $i$ ...
12
votes
1answer
170 views

Efficiently selecting the median and elements to its left and right

Suppose we have a set $S = \{ a_1,a_2,a_3,\ldots , a_N \}$ of $N$ coders. Each Coders has rating $R_i$ and the number of gold medals $E_i$, they had won so far. A Software Company wants to hire ...