Questions tagged [search-problem]

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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1answer
131 views

String Search - how to find the “most” accurate string?

Assume I have the following list of companies: Apple Big Apple Google Then I have this sample string: Big Apple is a company that is trying to be the next Google. Given the list of companies and ...
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5answers
974 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 ...
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0answers
28 views

Cyclic finite scheduling algorithm

I have a scheduling problem with the following specifications: A single machine is used. $n$ jobs $\mathbb{J} = \{J_1,...,J_n\}$ are available from the start $t = 0$. Each job can be executed several ...
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1answer
60 views

Why do we use DAG rather than trees to represent search space of a search problem?

I saw people use DAGs to represent the search space of a search problems like the travelling salesman problem. Why is this better than the tree representation? Is the reason to save memory space on ...
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1answer
16 views

Are there search problems that cannot be written as decision problems?

I'm not sure whether the distinction between decision and search problems has a deeper significance or if it is just concerns the immediate answer to the problem. Of course, if you have a finite ...
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1answer
1k views

Algorithm to create dense style crossword puzzles

I am working on creating a program to generate dense American style crossword puzzles of grid sizes between 15x15 - 30x30. The database of words I'm using ranges between 20,000 and 100,000 words of ...
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1answer
27 views

AI Search - State in the toy vacuum problem

I have been reading about AI search, specifically the toy vacuum cleaner problem and I would like to code an example of this but I am finding the description of the state hard to get my head around. ...
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1answer
55 views

Number of sentences and sentential forms generated by a grammar

In this question, I'm considering only "finite grammars". A finite grammar can only produce a finite number of distinct sentences. The following grammar is finite in my definition: ...
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3answers
8k views

Minimum number of tree cuts so that each pair of trees alternates between strictly decreasing and strictly increasing

A gardener consider aesthetically appealing gardens in which the tops of sequential physical trees (eg palm trees) are always sequentially going up and down, that is: ...
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3answers
261 views

Does White never lose in Chess if Chess is solved?

If the machine has enough memory and speed as to compute all states of the Chess game in a reasonable time, can a player with the white pieces - operated by a machine - lose a game?
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1answer
165 views

3Sum Why this O(nlogn) solution doesn't work?

I have been doing LeetCode and tackled the problem of the 3Sum and first I tried to do a O(nlogn) solution and after seeing the proposed solution I see that the solution is $O(n^2)$ or $O(n^2 \times \...
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0answers
99 views

Graph traversal problem touching every node exactly once

Is there a name for the problem: Suppose you have a connected, undirected graph; find a path that touches every node exactly once. This is basically the complement of the Hamiltonian Path problem, ...
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1answer
58 views

Definition and example of search problem

I searched the pages a lot about the search problem but didn't understand much, so please make it clearer for me. WIKIPEDIA: In computational complexity theory and computability theory, a search ...
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49 views

2 Partition Problem

I want to solve the two partition problem (https://en.wikipedia.org/wiki/Partition_problem) using an uninformed search algorithm (BFS or uniform cost). The states can be represented by three sets S1,...
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0answers
27 views

Transits directions search

Data Description : A database consisting of many Transits. Each transit has its own Path (both forward and backward), and each path has a set of Stops. Each stop consists of the position and the ...
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1answer
27 views

Recover a matrix with minimum number of queries

Alice has a matrix $A \in \{0,1\}^{n \times m}$ such that the sum of each row is $1$. Bob tries to find the indices of the ones (he knows that the sum of each row is $1$). The type of questions Bob ...
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0answers
143 views

Should a prefix tree (trie) node store only a single character or a string?

I've just implemented a Trie and I thought it would be a good idea to store strings in the Trie nodes in contrast to storing single characters. Storing strings is for sure more space-efficient and ...
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1answer
24 views

Do we understand when metaheuristics are optimal? (gradient descent & simulated annealing in particular)

Gradient descent sometimes works better than simulated annealing and vice versa. Are there conditions under which we can prove that, given perhaps a restriction on the set of allowed algorithms, one ...
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1answer
57 views

Finding lost bottle (algorithm problem)

The question is as follows: A scientist creates a new compound, called compound A, that will explode 10 days after being mixed with compound B. This compound A was stored in a label-less bottle on ...
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0answers
58 views

How to maximize $f$ while minimizing $g$ at the same time?

Lately, I have been dealing with a problem that I didn't know how to name it to solve it properly. The problem is as follow: let's assume that we have a set of elements $A$. And, we have two ...
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1answer
49 views

What does the search problem imply about the decision problem?

Let $\Pi_{dec}$ be an NP-complete decision problem and let $\Pi_{opt}$ be its corresponding optimization problem. Assume $\Pi_{opt}$ can be solved in polynomial time. What does this imply for $\Pi_{...
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0answers
20 views

A data structure for efficiently finding nodes relative to other (ex: if a node is earlier in a list than another node)

Suppose we have N elements, which we'll treat as a simple object. Is there a data structure I can use that will allow me to see which node appears earlier based on ...
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1answer
54 views

Finding maximal cardinal independent set given oracle

The problem is given an oracle $O(G, k)$ that would say if graph G contains IS of size k devise an algorithm for finding independent set of max cardinality that makes poly number of calls to the ...
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2answers
457 views

search problem vs optimization problem

This is mostly a terminological question: Is there a fundamental difference between "optimization problems" and "search problems"? Apologies if this is an obvious question As I ...
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2answers
253 views

Fastest algorithm to find whether a list contains a word?

Given an unordered list of words, what's quickest way to test whether a certain word is in that list? I can't think of another way to do this other than just going through each element in the list ...
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0answers
19 views

Beam search in the context of Genetic Algorithm

As per Machine Learning, Tom M. Mitchell, Indian Edition, pp. 249-262, it is mentioned that "genetic algorithms employ a randomized beam search method to seek a maximally fit hypothesis". I have ...
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1answer
1k views

Find an element in sorted 2D-array (matrix)

Given an $N\times N$ array, where elements are decreasing in every row and every column. What is the fastest way to find the $(i,j)$ of a given element if it exists in the array, or return no if it ...
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39 views

Breadth-first traversal: difference between generation and expansion

The question here is to find a path from A(rad) to B(ucharest). I'll be using the initials of the cities in the picture instead of their full names. Some ground-rules: we're traversing in ...
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1answer
114 views

I am looking for an algorithm that can find the best possible combination of inputs, in order to determine the optimum output

So as the title poorly implies, I'm looking for an algorithm that can accomplish the following task (as an example): Given the inputs A(1:100), B(1:100), C(1:100), that can take on any value between 1 ...
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2answers
96 views

Proving that a set of operations can't generate one integer from a given one

Given two numbers, $n$ and $m$, are there some mathematical methods of deducing $m$ from $n$ using limited number of elemantary operations? Example: 335 can be deduced from 2000 using division by 2, ...
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1answer
106 views

Efficient search for solving a Jigsaw Puzzle?

I believe that solving a Jigsaw puzzle is in general NP-complete based on the two questions linked below. However, I'd like to implement a heuristic algorithm that works well in practice. Let's ...
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1answer
29 views

Hardness of FNP vs Choice of Verifiers

A (T)FNP problem is induced by a NP language, say $L$. Usually in the notion of verifers, we define $L=\{x:\exists y,V(x,y)=1\}$, where $V$ is a poly-time verifier. The function version would be ...
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1answer
91 views

Repeated String Match: need help to understand the maximum number of repeats needed to be looked at

There's this question on LeetCode (link): Given two strings A and B, find the minimum number of times ...
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2answers
211 views

Interesting logic problems

I've just began a course on logic and learned the following : De Morgan's laws Normal forms How to represent a logical formula (using or, and, not operators) using binary trees How to get the ...
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1answer
161 views

Search on Conformant Problem: solution for subset of a belief state

I am having trouble understanding the following statement. I have understood why in a sensorless/conformant problem, if there exists a solution (a sequence of actions) for a belief state $b$, then it ...
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0answers
129 views

How to accomodate decision trees with infinite options

I know that once I have a graph or decision tree representation of a problem, there are many different ways I can get a computer to solve the problem. They're called search algorithms, and go by names ...
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0answers
23 views

fastest way to find matching pattern

I have several series of integers (vectors) that could be plotted at equal distances apart: ...
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2answers
373 views

Efficient way to find matching date ranges?

We have a set of problems involving date ranges - a pair of dates representing a start date and an end date. In some places, we have say 1000 of these and need to find the ones that overlap a separate ...
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1answer
61 views

Give a Search Problem in co-NP

Ex.1. Give a Search Problem whose deciding Problem is in co-NP. Assuming 3SAT is in NP then asking wether a given Boolean formula has a Solution is a search problem in NP right? Then would asking ...
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1answer
2k views

Babyface vs Heel

So here's the question: "There are two types of professional wrestlers: "babyfaces"("good guys") and "heels"("bad guys"). Between any pair of professional wrestlers, there may or may not be a rivalry. ...
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1answer
294 views

reducing a decision problem to a local search problem

Lemma 4 in How easy is local search by Johnson, Papadimitriou, and Yannakakis, states: If a PLS problem is NP-hard then NP = P So assuming L is a PLS problem (polynomial local search problem) that ...
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4answers
636 views

Are there any optimization problems in P whose decision version is hard?

Normally to show that an optimization problem is hard, we show the corresponding decision version of the problem is hard. However, is this sufficient to support the conclusion? Does there exist any ...
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2answers
1k views

Finding a local peak in an array in O(log N)?

So I watched a couple of videos regarding this and the divide and conquer made sense to me. But I am still not convinced as to how recursing on the side with the larger number guarantees us the ...
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1answer
261 views

Algorithm to organize a tournament where the team componentes change each round

So, I was tasked with creating an app that generates the schedule of a doubles tennis tournament (i.e., teams of two) in a way that, by the end of it, everyone would have played against the rest of ...
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1answer
24 views

Name of algorithm: When looking for an optimal element in a list, contionusly adapt the acceptance threshhold

I'm looking for one of two closely related algorithms. In both, you have a list of elements, of which you have to choose one by some scoring method. In the first variation, the list is infinite and ...
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3answers
20k views

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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0answers
19 views

Search techniques to find desired output with complex interdependencies

I am trying to generate output consisting of three-tuples (A,B,C), where A,B, and C are three different datatypes representing different values. I also have a collection of functions $f_i \in F$ ...
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3answers
2k 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 ...
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1answer
58 views

Alternatives to evolutionary computing for structure, design and policy optimization (optimal structure search)?

I once had this question https://math.stackexchange.com/questions/1083338/structural-design-meta-optimization-is-there-mathematical-theory-optimiza about the methods for finding optimal structures, ...
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0answers
102 views

Is there an analysis of the creation of axioms for a mathematical structure as a computational problem?

Historically, what has happened is the following: There is a "mechanical" structure, most importantly, arithmetic, which operates according to a set of well-defined rules that a stupid computer can ...