For questions about various search algorithms.

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1answer
13 views

Prove that search in matrix takes mor than n comparisons

Let us call matrix $A$ ascending if $A_{kl}\ge A_{ij}, i \le k, j \le l$ for every $k$ and $l$. Given a number $x$ prove that determining whether $x$ is in an ascending matrix or not takes more than $...
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0answers
24 views

Enumerate 'one number from each set' from a set of sets in order of increasing sum.

This question is somewhat similar to: Algorithm wanted: Enumerate all subsets of a set in order of increasing sums but has a significant difference in that instead of enumerating all subsets of a set, ...
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0answers
22 views

How do you calculate search spaces like tic tac toe?

I'm studying search spaces and I've been looking through the internet and can't find relevant info on how to work it out myself, the sources I found give a bad explanation of it, and do not explain ...
0
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1answer
18 views

Calculating the amount of times a binary search could run (worse case) without a calculator/calculating base 2 logs without a calculator.

Ok so I had a question on a test that I had to do without a calculator. And I can not figure out how in the world I am supposed to do it without a calculator. The question asked to find how many ...
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1answer
32 views

Minimum number of steps required to visit every “special” point on a rectangular gird

I am stucked at this problem: Suppose we have the following grid configuration (or matrix) $G\in \Bbb{M}^{\{0,x,y\}}_{m\times n}$ (I.e $G$ is a matrix that have $m$ rows and $n$ colums over the ...
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0answers
20 views

Uniqueness of spanning trees made using search algorithms?

For undirected graphs, the corresponding spanning trees can be obtained using various search algorithms like Depth-first search algorithm , Bredth-first algorithm, etc. I am not sure whether the ...
4
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3answers
71 views

Minimum number of steps required to visit every corner of a rectangular grid

I am stucked at this problem: Suppose we have the following grid configuration (or matrix) $G\in \Bbb{M}^{\{0,x,y\}}_{m\times n}$ (I.e $G$ is a matrix that have $m$ rows and $n$ colums over the ...
0
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0answers
18 views

3SUM problem solution on the basis of cubic function and a line?

The 3SUM problem formulation: in a given set of n real numbers find 3 elements that sum to specified value S. I am trying to understand mathematical solution of the 3SUM problem based on a polynomial ...
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2answers
40 views

How to prove $\frac15 n^2-42n-8\in Ω(n^2)$?

Here is my procedure: So we want to prove $\exists c\in\Bbb{R^+}:\ [\exists B\in\Bbb{N}:[\ \forall n\in\Bbb{N}:\ n\ge B\rightarrow \frac15 n^2-42n-8\ge cn^2]]$ Taking $B=1$. We have $\frac15 n^2-42n-...
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1answer
27 views

How to implement an algorithm for specific kinds of search in a graph

Imagine i have a graph called G. G has some parts. In one part, every node describes a person. I have another part in G which contains interests as nodes. ( Imagine that person A likes music. So, ...
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0answers
25 views

What is the maximum number of times that absolute value of neighboring difference is larger than a threshold?

Suppose I have a sequence of data $x_1$, $x_2$, ..., $x_N$. Suppose for a particular value $X$, and for a particular interval $m$, the number of times that $|x_{i+m}-x_i|>X$ ($1\le i\le N-m$) is $...
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0answers
10 views

Searching if a value is returned by a function defined for 2-D lattice points

Two functions $f:(x, y) \rightarrow \Bbb N$ and $g:(x, y) \rightarrow \Bbb N$ are defined where $\Bbb N$ is set of positive integers and $x, y \in \Bbb N$. Properties and relations $g(x, y) \ge g(x-...
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0answers
23 views

Exhaustive Search

Suppose you have a vector of array with N elements, and each element can be an integer between 0 and M. For example, "1, 3, 0, 4, 0" where N = 5 and M = 4. I want to find this array by just doing an ...
1
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1answer
100 views

Weakly unimodal function using Golden Section Search

I was going through the Golden Section Search https://en.wikipedia.org/wiki/Golden_section_search and as I understand it should work for every unimodal function. Here, the definition of unimodal ...
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0answers
38 views

Improving Simulated Annealing based on Measure of Goodness

can anyone answer this question or direct me to a reference that can help? Simulated Annealing returns the current state when the end of the annealing schedule is reached and if the annealing ...
1
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1answer
29 views

Does this search method exist and what is it called?

I would like to search some function $f(x)$ "greedily" for a certain condition. Assume the condition $c = f(x_1)$ returned by this function is currently false and I can increase the input $x$ to the ...
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0answers
20 views

Binary search for the worst case.

I want to analyze binary search for the worst case, completely mathematically without any ellipses(...). I solved out the recurrence of the binary search. $$ T(n+1)=T(n/2)+C $$ I've already searched ...
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0answers
11 views

2d search with high cost

I have a function f(x,y) that returns a fitness value, but calculating f(x,y) is very costly, and I expect a fair number of local maxima that are much lower than the global maximum. I do, however, ...
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0answers
22 views

How does Best First Search Calculate the Heuristic Values in the Graph

I understand that Best First Search uses a sorted open list based on Heuristic Values of the Nodes (priority queue) and a closed list.But how are these Heuristic values of the Nodes calculated? The ...
0
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3answers
326 views

Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
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0answers
22 views

Optimally exploring a 2d grid

Given a 2D grid and an unknown starting location, what is the best way to search every node? The size of the grid would be known prior to starting but the method should scale easily.
1
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1answer
41 views

Exploiting geometric invariants via group theory

Let $T$ be the set of all plane triangles. The problem is to find $t \in T$ s.t.h. a predicate $P(t)$ holds. At present, I'm doing this by a form of randomized search procedure (effectively via a ...
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1answer
27 views

Need help understanding a simplification in a simultaneous search model.

The problem I am trying to solve is $\max_{k \in \mathbb{N}} \int_0^1 u d F(u)^k - ck$, where the associated utility is an iid random variable U following $F(\cdot)$ on [0,1]. $c > 0$ is the ...
2
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1answer
43 views

Find the three closest surrounding neighbors from a data

I have a data of coordinates $x$ and $y$ where we know the range of both variables, e.g. $(x,y)\in[0,1]^2$. So for a given any random point $\theta_0=(x_0~~y_0)^T$ in the range of $x$ and $y$ I would ...
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0answers
77 views

How to determine size and height balance of binary search tree?

I've been reading/ learning binary search trees and I've been stuck on the following question for a while now. I have the following tree, how do I determine the height and size balance of it? How do ...
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1answer
188 views

Searching Algorithm

A company database has 10,000 customers sorted by last name, 20% of whom are known to be good customers. When looking up a customer’s record in the database, the good customers account for 60%. Two ...
0
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1answer
54 views

A mathematical expression for “grid search”?

I've got a question whether there is a mathematical expression for a grid search? I have two parameters a and b in [0;1]. Depending on the values of a and b, I get a value for my function (the value ...
2
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0answers
25 views

n-dimensional searching alogrithm

If you want to store various points in a $n$ dimensional (here $n=2$) space. Is there a possibility to do that with a tree (as a binary-tree for $n=1$ is usually used) for efficient and fast finding ...
10
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1answer
224 views

The “find my car” problem: proper interpretation and solution?

This has been asked at least twice here, but both questions have accepted answers which are wrong. I don't really know any good way to draw attention to the question besides asking again and being a ...
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2answers
88 views

How to use binary search to find a function

I am reading somewhere that $$(\phi'(y))^{-1}=y^{-c_1}+y^{-c_2},$$ $c_1,c_2$ are some numbers, can be solved for $\phi$ using binary search. I am surprised because binary search binary search is used ...
0
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1answer
119 views

Infinite Search Tree Probibility

I have a question on Search Trees. I have a balanced, infinite, search tree. If you check a node at level $l$, the probability of finding a solution at that node is $p^l$. Questions The first ...
4
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1answer
80 views

Spacing of fence posts with minimal distance to other fence posts

Definition 1: A "fence" is a set of "fence post positions", where each pair of adjacent positions has the same difference (the spacing), e.g. $\{1,2, 3, 4\}$. A fence is described by three values ($\...
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1answer
141 views

How to search between $n$ candidates from unknown position?

It might be involved more with search algorithm but I cannot think of any of them. Here is the problem: You are in a corridor that stretches infinitely in both directions. Your room is somewhere ...
3
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1answer
744 views

Choose a k-subset such that its elements 's gcd is maximal

Given $n$ positive integer and a positive integer k. How to find a subset of size k such that its elements 's gcd is maximal (just give the maximum value of gcd is okay). Example: Give $3$ integers ...
1
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1answer
23 views

Binary search in merged arrays.

Given two arrays, sorted by ascending. Result array is first array and second at the end of first. Example: [1, 4, 7, 11] and [2, 3, 5]. Result array is [1, 4, 7, 11, 2, 3, 5]. How to find element ...
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0answers
45 views
0
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1answer
46 views

How to extract all the points from a noisy surface?

I have points representing a bridge like in this picture: My goal is to get all the points that are in the red box. These points all share a common surface that is not necessarily planar. The ...
2
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0answers
284 views

A* vs D* vs Dijkstra [closed]

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* ...
0
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2answers
331 views

Shortest Path between two vertices of a weighted, undirected graph IN LINEAR TIME

Studying for an algorithms test, and a surprisingly simple problem has me somewhat stumped. The following is the question: My issue has been - looking online, everyone uses this kind of problem to ...
1
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1answer
154 views

Searching for random items in a set of lists

This is a programming question, but I'm interested in the math behind it so I think it's better asked here. Say I have a list of items and I'm looking for one item in the list that satisfies a ...
0
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0answers
45 views

How to search for an object in more efficient way?

I have a doubt how to check if structure contains an object. Simple sketch of my structure: Root - is a group which can contain groups, keys, values. Group - can contain groups keys, values. Key - ...
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0answers
37 views

State Space Search

I searched in the web about simple example about State Space Search, but I didn't find any simple and clear one. Can anybody explain to me what State Space Search about by a simple example? Thanks ...
1
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1answer
32 views

Having objects trajctories and directions how to find where objects traverse same path?

I have N objects that travel on some trajectories (unique for each object). At each agent curve point we can get object speed (direction). Having some distance ...
1
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1answer
565 views

Breadth-first search tree

It seems intuitive, and is actually proven in many books, that each path from starting vertex to another one in any search tree of a breadth-first algorithm is the shortest. However, I couldn't find ...
1
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1answer
2k views

Term-document vs document-term matrix [closed]

I am not sure if this is the right website to ask this question but I cant figure out where else to get the answer so, please, dont be mad :-) As my bachelor thesis/project, I am trying to construct ...
2
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0answers
171 views

Partition minimizing maximum of Euler's totient function across terms

Given natural numbers $M$ and $N$, I'd like to find a partition of $2^N$ with $M$ or fewer terms, $t_1 + t_2 + ... + t_M$, such that $\max(\phi(t_1), \phi(t_2), ..., \phi(t_M))$ is minimized, where $\...
0
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1answer
44 views

Trivial case of $s \in T$

I was reading paper A Formal Basis for the Heuristics Determination of Minimum Cost Paths in section B "Some Definition About Graphs" there is footnote that say "We exclude the trivial case of $s \in ...
4
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1answer
2k views

Median of medians algorithm

I am referring to the algorithm presented here used to find a good pivot: http://en.wikipedia.org/wiki/Selection_algorithm#Linear_general_selection_algorithm_-_Median_of_Medians_algorithm My ...
0
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1answer
681 views

Help in understanding search of Vantage-Point tree

This is my reference: http://stevehanov.ca/blog/index.php?id=130 A vantage-point tree is a way of organizing a set of points so that finding the n-nearest neighbors is as efficient as possible. It ...
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0answers
60 views

How to formulate a best-search algorithm limited by a count of nodes visited?

The problem I'm doing a search by computer program. Each node takes about 5 minutes of wall time to get a result so I'm looking to carefully choose the nodes to inspect so as to find the best result ...