# Tagged Questions

A class of computational problems. Where decision problems call for a yes-or-no answer, search problems are looking for an object satisfying a certain property.

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### Symmetry in Pattern Databases

I am trying to understand the use of symmetry in pattern databases (Heuristics, single agent search). This is too specialized of a topic to find common videos or explanations in general. I read the ...
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### Classification with optional/catchall attributes

Context Let $S$ be a set of objects, each object $S_k$ containing a set of attributes $A_k\subseteq A$, where $A$ is a global set of attributes. Suppose each attribute $a_k\in A$ can take on integer ...
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84 views

### Reduce set partition search to decision?

I'm a little lost and don't know how to approach this problem. Show the partition search problem can be poly-time reduced to the partition decision problem, the partition decision problem takes ...
0answers
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### Neighbourhood design in Variable Neighbourhood Search

Variable Neighbourhood Search (VNS) is a metaheuristic for solving (combinatorial) optimization problems. It iteratively explores growing neighbourhoods to find better local optima in each iteration. ...
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### An optimization in this algorithm

I'm trying to implement an autocomplete feature for a search engine. I have a database of words(stemmed) that occur in the documents that I have. what I'm doing is: Constructing a graph with words ...
1answer
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### Efficiently locating the maximum value in interval over large amounts of data points

I have a set of $n$ two-dimensional data points $(x_i,y_i)$. I want to efficiently answer the following query: Given an arbitrary interval of $x$-values, find the highest and lowest points within ...
1answer
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### Informed search with a lower-bound heuristic?

I am well aware of informed graph / tree search strategies for optimal solutions when one has an admissible heuristic - i.e. one that never overestimates the minimum cost from a node to any goal state....
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### How can I solve this problem which seems related to the Kth-heaviest subset problem?

Instance: Given a matrix of size $m\times n$ of positive real numbers, $m$ real numbers $L_i$ for all $i\in\{1,\cdots,m\}$ and an integer $k$ less or equal than $n$. Question: Is there a subset of ...
1answer
89 views

### Maximize ratio of sums

I have a $2 \times n$ matrix of positive integers, where the elements are denoted by $a_{ij}$ for all $i$ in the set $\{1,2\}$ and for all $j$ in the set $\{1,\ldots,n\}$. I would like to select a ...
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1answer
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### Searching the space of permutations

I'm given n objects, and a set of n permutations of these n objects (out of n! total permutations). There is a true underlying permutation, which I know is one among the set of n permutations, but I ...
1answer
103 views

1answer
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### Searching through a heap complexity

Pretend you want to search through a max-heap to find a specific element. I know there is no such option but still... Would it take worse case O(n) or O(logn) time? I am assuming O(n) since the ...
4answers
346 views

### Can finding a witness be NP-hard even if we already know there is one?

The common examples of NP-hard problems (clique, 3-SAT, vertex cover, etc.) are of the type where we don't know whether the answer is "yes" or "no" beforehand. Suppose that we have a problem in which ...
3answers
84 views

### Graph cycles on 40 vertices

I'm trying to create an algorithm in polynomial time, that detects wether or not a graph is in a language. The language specifies that a graph is only part of this language if it has a cycle on 40 ...
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185 views

### What data structure would help find nearby coordinates quickly?

I need to write a program that does the following: Take an input list of objects whose properties include latitude and longitude to, say, 5 decimal places Store them in a data structure once Provide ...
1answer
458 views

### Artificial intelligence - bridge and torch problem

I am doing a artificial intelligence course as part of my computer science degree. I am stuck on a question about searching. The question is a version of the Bridge and torch problem. Five people ...
1answer
149 views

### Efficiently count frequency of n-grams at start of words

I have a text file with all possible 5-grams (26^5 = 11.881.376) organized in rows as: aaaaa aaaab aaaac aaaad ..... and I have a txt file (organized in rows) with all English words. I have to find ...
1answer
275 views

### How to do high performance string matching when comparing unordered sets of tokens [closed]

This is the problem: I have some strings stored in the database. Each of the strings can be seen as a set of tokens separated by comma with no repetition (I mean a token cannot appear more than one ...
1answer
67 views

### Using A* search with different heuristic values

I am currently trying to use A* to create cyclical routes (for plotting driving routes of set distances). I want to find a driving route from my start location that is as close to my specified length ...
1answer
269 views

### Selection problem on the union of two ordered dictionaries

Suppose we are given two ordered dictionaries S and T each with n items, and that S and T are implemented by means of array-based ordered sequences. Describe an O(log n) time algorithm for finding the ...
1answer
90 views

### What is the lower bound for finding the third largest in a set of $n$ elements?

The problem is easy to describe: What is the lower bound for finding the third largest in a set of $n$ elements? Particularly, do we have to know both the largest and the second largest for ...
1answer
58 views

### Whats the name of this search game?

I am struggling in finding the name of this game (in order to find research papers related to it in the literature). Given an initial word $X$ and a target word $Y$, what is the minimum number of (...
1answer
74 views

### Generating hard puzzles for a backtracking snake

Let $M$ be a matrix of height $h$ and width $w$. Each entry of $M$ is an integer. There is a snake that starts from the "left side" of $M$, and its goal is to reach the "right side" of $M$. To get ...
1answer
403 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 ...
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### Given a graph, finding if a node has three adjacents from a node subset $N$

Given a graph $G = (V,E)$, assume that we have two disjoint vertex sets $N = \{n_1, n_2 ...\} \subset V$ and $P = \{p_1, p_2, ...\} \subset V$ such that $N \bigcup P \neq V$. I want to find if there ...
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54 views

### TF-IDF query engine in context of terms weight

I'm looking for public algorithm which gives the engine these abilities: Query by ranked terms Limit outcome by date/time range Basically, i'd like to concentrate articles (generally ...
1answer
691 views

### Time complexity of 8-queen, by placeing one by one without attack

I am new to artificial intelligence. I have been trying to analyse the time complexity of 8-queen, by placing one by one without attack. One approach to achieve goal state is to "add a queen to any ...
1answer
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### How feasible is it for a non-distributed web crawler running on consumer hardware to search the internet? [closed]

I am looking for an automated way to answer the question: what are the URLs on the world wide web that contain at least two strings from a set of strings. So if I have a set of strings {"A", "B" and ...
2answers
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### Decomposing the search problem into several small problems

I am looking for papers/methods (or at least problem examples) where the original search problem $P$ can be solved by either: Searching through the original graph. or By decomposing it into several ...
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40 views

### Search problems that can also be solved by junction trees and searching cliques

Assume having a graph $G_{variables}=(V,U)$ where $V=\{v_1,v_2,…,v_n\}$ is a set of variables; each variable $v_i\in V$ is associated with a set of possible values (it's domain) $dom(v_i)$. Let $P$ ...
2answers
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### Artificial Intelligence: Condition for BFS being optimal

It is said in the book Artificial Intelligence: A Modern Approach for finding a solution on a tree using BFS that: breadth-first search is optimal if the path cost is a nondecreasing function of ...
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210 views

### Does FNP-complete = NP-complete?

I can't seem to find this stated explicitly anywhere, which makes me wonder if I have it all wrong. So first, let's say we view problems in NP as degenerate problems in FNP, where the codomain of the ...
2answers
819 views

### Worst case scenario in binary search tree retrieval

Well, i have a binary search tree $T$ that is equilibrated by height witch has $2^d+c$ nodes ($c<2^d$). What is the number of comparisons that will occur in the worst case scenario, if we ask ...
1answer
167 views

### Efficient algorithms for finding a region in $\mathbf R^2$

This question is an extension of a previous question I've asked. Consider the rectangle $a<x<b , c<y<d$ in the $\mathbf R^2$ plane. Each point in this rectangle can be of kind #1 or #2 (...
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66 views

### LInear time algorithm to find the diameter of a tree [duplicate]

This is NOT HW, this is from Skienas book, and I just couldn't solve it at all. Please give me a hand here, in understanding and solving it, thanks. Let G = (V, E) be a binary tree. The distance ...
2answers
748 views

### Uniform-cost Search Problem

Suppose that we take an initial search problem and we add $c > 0$ to the costs on all edges. Will uniform-cost search return the same answer as in the initial search problem? Definitions: Uniform-...