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.

Filter by
Sorted by
Tagged with
30
votes
2answers
10k views

Optimization version of decision problems

It is known that each optimization/search problem has an equivalent decision problem. For example the shortest path problem optimization/search version: Given an undirected unweighted graph $G ...
14
votes
1answer
410 views

Coverage problem (transmitter and receiver)

I try to solve the following coverage problem. There are $n$ transmitters with coverage area of 1km and $n$ receivers. Decide in $O(n\log n)$ that all receivers are covered by any transmitter. All ...
11
votes
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 ...
10
votes
2answers
359 views

How do I classify my emulator input optimization problem, and with which algorithm should I approach it?

Due to the nature of the question, I have to include lots of background information (because my question is: how do I narrow this down?) That said, it can be summarized (to the best of my knowledge) ...
9
votes
2answers
299 views

Find the central point in a metric-space point set, in less than $O(n^2)$?

I have a set of $n$ points which are defined in a metric space – so I can measure a 'distance' between points but nothing else. I want to find the most central point within this set, which I ...
8
votes
2answers
9k views

Is using a more informed heuristic guaranteed to expand fewer nodes of the search space?

I'm reading through the RMIT course notes on state space search. Consider a state space $S$, a set of nodes in which we look for an element having a certain property. A heuristic function $h:S\to\...
8
votes
1answer
572 views

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 ...
7
votes
2answers
1k views

Is there any strategy to brute force search?

I don't know how to state it elegantly, but basically, I want to implement a brute force search algorithm, but there are many different ways that I could enumerate through the search space. This ...
6
votes
1answer
637 views

Should you use Genetic algorithm for an extremly large unstructured search space?

My search space is discrete and in the order of $10^{1360}$, with a probably very complex fitness surface. Is it hopeless to attempt to use GA for such a problem? One fitness evaluation could take 1-3 ...
6
votes
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: ...
6
votes
1answer
282 views

Is there a polynomial time algorithm to determine whether an 'up down' language is 'emptible'?

Definitions: An up down language is a language whose alphabet is a set of pairs, but not characters, of two characters, where the one character in the pair is the opposite of the other character in ...
6
votes
1answer
847 views

(Nontrivial) Algorithms for finding the third largest element of a set

According to the lecture note by Jeff Erickson, the lower bound for finding the third largest element of a set of $n$ distinct elements is open. See the related post: What is the lower bound for ...
6
votes
1answer
270 views

Can deterministic Turing machine beats/wins (if possible) the “Bombs and Levers” game in polynomial time?

The description of this game is already exists in this link I am quoting from this link the description of the game to ease the reading of this question: In a game, where there are m active bombs, ...
6
votes
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 ...
6
votes
1answer
313 views

BPP search: what does boosting correctness entail?

It is not really clear to me, how and if I can do boosting for correctness (or error reduction) on a BPP (bounded-error probabilistic polynomial-time) search problem. Can anyone of you explain me how ...
6
votes
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 ...
6
votes
1answer
120 views

Partitioning an undirected, unweighted, square planar graph paths that join certain pairs of nodes

I am trying to find a way to efficiently solve a puzzle that I play a lot by turning it into a graph partitioning problem (which is basically is in its actual form). I know that generally, graph ...
5
votes
5answers
5k views

Algorithm for finding two smallest numbers in an array

I was just thinking today that the best approach to find two smallest numbers in any array would be to first sort(ascending order) it with some efficient algorithm like ...
5
votes
4answers
2k views

Divide an integer into the sum of consecutive positive numbers

Today I am trying to solve an classical problem: For any $n\in \Bbb{N}^+$, If it can be represent as the sum of consecutive positive numbers, find out them. For example: $$15 = 1+2+3+4+5$$ $$15=...
5
votes
4answers
637 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 ...
5
votes
1answer
278 views

Fastest search algorithm in a sorted list with certain error rate-limiting constraints

This problem came up during the Google CTF 2017. For background information about the challenge you can search for GoogleCTF A7 ~ Gee cue elle. Problem description:...
5
votes
1answer
358 views

What is the complexity of finding a regular expression equivalent to a given DFA?

I had taken a course long ago on complexity theory. I only remember basic things, so I am reading "Introduction to the Theory of Computation by Michael Sipser". The book in its first chapter ...
4
votes
1answer
807 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 ...
4
votes
1answer
270 views

Does NP-completeness require to find the solution?

In the paper "Computing Equilibria:A Computational Complexity Perspective" by Tim Roughgarden, they consider the problem: Problem 2.1 (Clique). Given a graph $G = (V, E)$ and an integer $k$: if ...
4
votes
2answers
2k 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-...
4
votes
1answer
474 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 ...
4
votes
2answers
68 views

Among $k$ unit vectors, find odd set with sum length less than 1

I have $k$ unit vectors in $\mathbb{R}^k$. Can I efficiently identify a set of $2n+1$ vectors $v_1, \dots v_{2n+1}$ such that $\sum_{i< j} v_i\cdot v_j < -n$ for any $n$ -- or determine that no ...
4
votes
1answer
876 views

Showing NP-hardness by reducing from a search problem

I'm comfortable with showing NP-completeness of a decision problem: just take some problem that is known to be hard and reduce it to your new problem. This establishes NP-hardness of the new problem. ...
4
votes
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 ...
3
votes
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?
3
votes
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 ...
3
votes
1answer
915 views

Solving cycle in undirected graph in log space?

Setting Let: $$UCYLE = \mathcal \{ <G> ~:~ G \text{ is an undirected graph that contains a simple cycle}\}.$$ My Solution we show $UCYLE \in L$ by constructing $\mathcal M$ that decides $...
3
votes
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, ...
3
votes
2answers
171 views

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 ...
3
votes
1answer
538 views

Weighted closest-pair-of-points problem

I want to solve the following optimisation problem (an approximation or heuristic would be helpful as well). I have two sets of points in the plane: $P=\left\{ p_{1},p_{2},\dots,p_{N}\right\} $ and $...
3
votes
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 ...
3
votes
0answers
202 views

How to minimize the sum of edge weight in the graph while keep the all-pair shortest path greater than a constant?

For example, if we have a graph G = (V, E) and a subset of vertices $U \subset V$. We can set $w(e)$ where $e \in E$ to be a non-negative real number. We want to minimize the total edge weight, but ...
3
votes
0answers
48 views

What data structure should I use for storing my data?

I am currently looking for a way in which I can store my data, and quickly look it up. What currently seem to be the best idea is to use a hash map. reasons: To identify what item I am looking for, ...
3
votes
1answer
86 views

Are there name and literature for this SAT-like problem?

Given $f : \{0,1\}^* \to \{0,1\}$ and $n \in \mathbb{N}$, we define $\textsf{Prob}(f,n)$ as the following problem: Find an $x \in \{0,1\}^n$ such that $f(x) = 1$. A machine solving $\textsf{Prob}(...
2
votes
2answers
142 views

Choosing nonzero entries from an array so no pair in same row or column

Suppose we have an $n\times n$ array $A$ of non-negative real numbers in which the sum of each row and each column is $1$. We want to find $n$ entries of the array $(x_1,y_1), \dots, (...
2
votes
3answers
173 views

Efficient algorithm to decide if a location is reachable

I am designing a game solver. I have a binary $m*n$ Matrix, where $0$ stands for a free space, while $1$ stands for an occupied space. In the game we move a ball that we will call $x$. The ball can ...
2
votes
1answer
11k views

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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
3answers
114 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 ...
2
votes
1answer
1k views

Heuristics for the $n$-puzzle

An admissible heuristic for an n-puzzle is the Manhattan distance. Now if the cost of a transition is equal to the number of the piece that is moved, is it true that the Manhattan distance is still an ...
2
votes
2answers
175 views

Is P = NP when solutions length is polynomially bounded by instance length?

I'm currently reading the book "P, NP, and NP-Completeness" by Oded Goldreich. I'm currently reading a chapter that's concerned with the "search version" of the P-vs-NP-problem, that is if finding ...
2
votes
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 ...
2
votes
1answer
2k views

Find all intervals that are contained in a query interval

Given a set of intervals $S = I_1, ..., I_n$, what is the fastest way to find all intervals of $S$ that are completely contained in an interval $I_\text{query}$? It should also support incremental (...
2
votes
1answer
2k 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 ...