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.

Search problems are a class of computational problems. Generally a search problem is of the form:

Given input $x$,
Find a $y$ such that $R(x,y)$ holds.

where $R$ is a binary relation. The $y$ does not need to be unique. By putting restrictions on the possible $y$s and the computational complexity of $R$ we obtain various class of search problems.

An example of a search problem:

Given a graph $G$,
Find a $C$ which is a maximal clique in $G$.

For algorithms for searching for an object satisfying a property please use the tags and .

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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 $G = (V, E)$ and two vertices $v,u\in V$, find a…
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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 reveivers and transmiters are represented by their…
com
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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 the we know the answer is yes, furthermore we can…
mba
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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 all varying lengths. The current algorithm I'm…
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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) as: What methods exist to find local optimums on…
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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 define as the point with the minimum sum of distances to…
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Minimum number of tree cuts so that each pair of trees alternates between strictly decreasing and strictly increasing

A gardener considers aesthetically appealing gardens in which the tops of sequential physical trees (eg palm trees) are always sequentially going up and down, that is: | | | | | | | | | | On the other hand, the…
Alan Evangelista
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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 don't know which one. An oracle however knows the…
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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 $h:S\to\mathbb{R}$ measures how promising a node is. $h_2$ is…
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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 it works? With BPP search, I mean a problem that…
LMG
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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 might be naive of me, but I imagine that how I choose…
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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 the depth of the node. The most common such…
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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 understand it, we can define the two as follows (note, I consider the…
user56834
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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 optimization problem which is easy but its decision…
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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, each one with a number above zero, and n standing…
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