Questions tagged [search-algorithms]

Algorithms for finding an element in some specified data-structure (most commonly, in a tree).

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Number of shortest paths between two nodes in undirected unweighted graph

I'm trying to devise a $O(|V| + |E|)$ algorithm to calculate number of shortest paths between $s$ and $f$ on a undirected, unweighted graph. Can someone please check my pseudo-code? Also, isn't $O(|V| ...
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Is the first distance that gets assigned to a node in BFS always the shortest distance?

Consider the following bfs pseudo code that calculates distances of all nodes from $s$ in graph $G=(V,E)$. I know that if $G$ was undirected and unweighted, then the above bfs would calculate correct ...
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36 views

Algorithm to find the path with minimum bending points on a square grid board

Let's suppose we have a square grid board like the one shown in the picture below: I'm wondering how I can find the path with minimum number of "bending" points (like the ones shown in red) ...
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Finding matches between an input string and a fixed set of strings

I need to compare an input string to multiple strings which I'll refer to as fixed strings, and you can assume the latter won't change. Comparison disregards letters with special characters, only ...
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Finding the Solution out of N possibilities

Suppose there are 10 (4x4) matrices, where the elements in each matrix are dependent on one variable ($\theta$) non-linearly. All the matrices are independent of each other, so there are 10 $\theta$s (...
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In RBFS, why should expanded nodes inherit F-value of their parent, if their f-value (g(n)+h(n)) is less than their parent's F-value

Here https://uk.wikipedia.org/wiki/RBFS and here https://www.eecs.yorku.ca/course_archive/2013-14/F/3401/slides/15b-RBFS.pdf it's said that f[s] ← max(g(s)+h(s) , f[node] ) Why is it so? I can see a ...
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Does this Hamming-like algorithm for solving a permutation of an address space have a name?

I'm working on reverse engineering the bit stream format of an FPGA, in particular regarding the address translation of the BRAM (block RAM), but the algorithm could in general be used for any ...
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32 views

Search algorithm for an expensive boolean function

I have the following problem. We have a boolean function $f$ that is expensive to compute for a given input. We need to find the smallest positive integer $n$ such that $f(n)$ is true. We don't know ...
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46 views

array empty cell search algorithm

I'm Telecommunication student so I don't have Computer Science background, just in case if my question looks stupid. Here is my scenario: Consider an empty array named ...
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40 views

How to search all possible combinations for a product?

I'm looking for the name of the problem stated below or, if available, even the algorithm to solve it. This is a hypothetical idea of mine, I don't actually have the necessary data to implement it. ...
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31 views

Best algorithm for Decisional 4-XOR problem?

Decisional 4-XOR Problem: Assume $M>>n$ (e.g. $M=50n$ ). Let $A_1,A_2,A_3,A_4$ be sets consisting of $M$-bit elements. Each set has order exactly $2^n$. Decide whether or not there exists $a_i \...
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Difference Between k-center and k-mean/median

I know that k-mean/median is to find a set $F$ that minimize $$\sum_{i\in C}\min_{j \in F} d(i,j)$$ Where $C$ is set of clients and $F$ set of facilities. (For k-mean you just square the distance). ...
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Using graph symmetries to speed up subgraph enumeration

I have an undirected graph $G$. It has some symmetries in the sense that I know it's automorphism group $\text{Aut}(G)$. I am searching for a specific subgraph defined by some constraints $\phi$ and ...
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33 views

Avoid Storing Keys in Key-Value Store by Replacing the Key with 128-bit Murmur3 Hash

I want to develop LRU key-value data store and in that wanted to get rid of space to store the key itself. Instead wanted to store a 128 bit murmur hash. The structure of data-store that I want to ...
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SMA*+: What if a removed node gets re-generated via another predecessor?

One last question came to me while reading the paper on SMA*+ about setting the $f$-cost of nodes being re-generated. Well, first, it looks like the part of the algorithm where we set the predecessor ...
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SMA*+: Usefulness of culling heuristics

The paper on SMA*+ proposes a very interesting idea of having a culling heuristic different from the full path cost estimation (so called $f$-cost). In the benchmark they use a culling heuristic equal ...
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SMA*+: f-cost estimation of re-generated nodes

I was reading the paper on SMA*+, which is very interesting as it implements most improvements I thought of when reading the paper on SMA*. But I have 3 questions that I think are related to my ...
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Is this a good way to arrange data in a tree?

I was recently learning about Binary Search Trees(BSTs) and thought it could be made even more efficient by making some changes. As binary search trees have numbers greater than the root node on the ...
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Create a data structure with D-SUCCESSOR running in $O(1)$

Given an integer $d$, I need to devise a data structure $S$ with the following actions: BUILD(S): build the data structure $S$ from $n$ elements in $\Theta(n\lg{n})$ INSERT(S, k): insert a new ...
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Remove a subsequence from a string and append it at the end

Consider the following operation on strings: pick a (not necessarily contiguous) subsequence, remove it and then append all the characters in the same order at the end. This operation preserves the ...
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Finding 2 nodes which sum equals twice their common ancestor in RBT in $\Theta(n\lg n)$

I have a red black tree, $T$, and I need to write an algorithm to find 2 nodes $x$ and $y$ so that $key[x] + key[y] = 2 \cdot key[p(x, y)]$, where $p(x, y)$ is the lowest common ancestor of $x$ and $y$...
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List the lengths of all the prefix-suffixes in $O(n^{1+\epsilon})$ time

A proper prefix of a string $s$ that is also equal to a suffix of $s$ is called a PS (prefix-suffix). Given a string $s$ of length $n$ is there an algorithm listing the lengths of all the PSs in $O(n^{...
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54 views

Parallel algorithm for finding the maximum in $O(\log \log n)$ time

With a CRCW (Concurrent Read, Concurrent Write) PRAM model, it is possible to find the maximum in an array containing $n$ elements with $n$ processors in $O(\log \log n)$ time. The algorithm is: If $...
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A beginner's question on programs that can search and calculate in very large sets

I am not in the computer science field and was looking for some guidance on books/papers/programs that allow me to learn how to design algorithms for problems that involve very large number of ...
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How to efficiently search a list of data structures with filtering support

I'm working on a project where I need to create search functionality that can efficiently search a list of data structures like: ...
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280 views

Average time complexity of linear search

It is usually assumed that the average time complexity of the linear search, i.e., deciding whether an item $i$ is present in an unordered list $L$ of length $n$ is $O(n)$ (linear). I have read ...
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79 views

How to do binary search on a path in a binary heap

I am trying to solve this question: Let's say you have a binary heap and an index $i$, design an algorithm that finds if a number $x$ appears in the path between the root of the heap and $heap[i]$ in ...
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63 views

How do I solve a search problem on an infinite graph?

I have a search problem that requires me to find a path from $v_s$ to $v_g$ in the graph $G = (V, E)$ where $v_s, v_g \in V$ are the start and goal vertices in a set of vertices and $E \subset V \...
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51 views

Is there a theorem that says when an array of numbers can be searched faster than linearly?

I'm familiar with binary search, but I'm interested in when a collection of numbers can be searched faster than checking them all one by one with any algorithm. Binary search requires sorting to work, ...
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Should your heuristic for an A* search algorithm be the same scale as your actual weights?

I'm a bit confused about the scale of heuristics for implementing A* search. $f(n)$ is the total cost of travelling to a node $n$. It is calculated by $f(n) = g(n) + h(n)$. $g(n)$ is the cost of the ...
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A very simple question about Admissible Heurisitcs

Given admissible heuristics f(s), g(s), h(s). It is true that max(f(s), g(s), h(s)) is still admissible.. but is it still admissible if its max(f(s), g(s) + h(s)). I believe it is not admissible but I ...
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Searching for the underyling affine transformation in a ridge function

Quoting from Wikipedia: A ridge function is any function $f:\mathbb{R}^d\rightarrow\mathbb{R}$ that can be written as the composition of a univariate function with an affine transformation, that is: $...
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109 views

Searching in sorted array with $O(\log n)$

Recently been practicing some recent exams, there was a problem I could not comprehend the given answer, the question is as follows: Suppose array $A[1..n]$ consist of $n$ distinct integers that is ...
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UCS and Dijkstra's algorithm do both of them give the minimal cost between two vertices?

i tried both algorithm to find the shortest path with minimal cost between two vertices,but most of the time Dijkstra gives a different path and the cost is smaller than the cost for the path UCS ...
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1answer
61 views

Minimal unsatisfiable core algorithm

Wikipedia says that There are several practical methods of computing minimal unsatisfiable cores. but I cannot find any. I suppose that “practical methods” means polynomial algorithms. Be careful, a ...
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Iterative Deepening DFS for DAGs

Does Iterative Deepening DFS only guarantee the shortest path for DAGs, assuming a visited list is used to prevent infinite cycles? I can't seem to find any answers online specifically related to ...
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How to modify the following Dijkstra/ Uniform-cost search to return the result for all end points?

I know there is a lot of code out there that does this, but in particular, I'm trying to modify the following code to not just return the goal node/ one end point, but all endpoints. How do I go about ...
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45 views

How to split the array into two subarrays with the smallest sum difference?

Given An array of elements, all elements are positive (unsorted, but sorting is not a problem if required) The objective: To create two subarrays, so that ...
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Scheduling Repeating, Flexible Intervals with Restrictions on Overlap

I work in 52:17 work:break intervals, as there's some evidence showing it's an effective way to structure the day. However, meetings or planned breaks often require shifting that schedule, moving, ...
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27 views

Search for specific element in sorted array

Given sorted array $A[1..n]$. We want to find an element such that $A[i]=3i+2$ in $O(\log n)$(binary search). I trying to relate to problem finding element in sorted array $A$ such that $A[i]=i$, ...
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44 views

If possible, use binary search to find an element in sorted array

Given sorted array $A[1..n]$, we want to find an element such that, $A[i]=i^2$,Can we use binary search to find such a element? My Attempt: initially, I read this link, but I can't understand the ...
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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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Search algorithm for multidimensional space with custom topology

First, let's start with the description of the problem in dimension 1: Let $T_0$ be a space with $n$ nodes organized in a tree structure, with $m$ of those nodes defined as target nodes. In this space,...
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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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31 views

Determine saving moves for a checked king

In my chess code I explore the whole tree of possible movements to find saving moves for a checked king. That is, for every one of the checked king's side pieces I search their whole tree of moves and ...
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Cycles of a multigraph with a property on the edges

Let $n$ be a positive integer. On a circle are arranged $n$ points $A_1$, $\ldots$, $A_n$. We put some arrows from $A_1$ to $A_2$, from $A_2$ to $A_3$, etc., from $A_n$ to $A_1$. On each arrow are ...
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Further papers or code on SMA*+?

I'm interested in the Lovinger and Zhang paper Enhanced Simplified Memory-bounded A Star (SMA*+). Are there any further papers on this algorithm or publicly-visible code (in any language) ...
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44 views

Algorithm chalenge: find minimum range to cover all houses with light

N houses are located on a straight street which has K streetlights. Each streetlight has range R. Given N and K how to find minimum value for R? N is an array containing location of each house. K is ...
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Find dominated or subsumed linear inequalities efficiently

Problem statement Given a set of $N$ linear inequalities of the form $a_1x_1 + a_2x_2 + ... + a_Mx_M \geq RHS$, where $a_i$ and $RHS$ are integers. The inequality $A$ dominates or subsumes inequality $...
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66 views

How does node expansion work in a graph for AI search?

I want to try and write an example that solves the problem of travelling from one location to another described in the book AI: A modern approach. The problem involves getting from a particular city ...

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