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### An efficient way to find a pair of unrelated edges

I'm writing a program which uses an undirected graph to represent certain social connections, and I'm trying to check whether or not it's contains a specific induced subgraph. Given a dense an ...
1 vote
84 views

### Why in Edmonds Karp or Ford Fulkerson Algorithm the time complexity of BFS or DFS respectively is O(E) rather than O(V+E)?

For these algorithms, the time complexity of BFS and DFS is O(E). I have gone through many websites and even the algorithm books, but I never got a clear idea of why it is O(E). It just says it's O(E) ...
32 views

I'm working my way through the graph section of Introduction to Algorithms by CLRS (3E,4E) and I came across the following proof: 3E: Lemma 22.2 Let $G = (V, E)$ be a directed or undirected graph, and ...
57 views

### Prove that BFS computes the shortest path from one vertex to another

I read in Algorithms in C by Sedgewick that we can easily prove by induction that breadth-first search algorithm computes the shortest path from one vertex to another (unweighted graphs or weighted ...
1 vote
121 views

### Goal-testing when node is "Generated" vs when node is "Expanded" contradiction (breadth-first search)

In my textbook "AI: A Modern Approach" it states that we expand a node to generate it's children. So I understand the definition of those two words as: Expand - Generate/create all the new ...
38 views

### Algorithm for detecting if H is a induced subgraph of G in O(n)

Say that I am given a graph $H$ and a graph $G$ where the maximum degree of $G$ is known. How can I use BFS to find out if $H$ is an induced subgraph of $G$ in $O(n)$ time? My current take is the ...
1 vote
34 views

### Special arcs - graph traversal

question is: given an unwighted nondirected graph G=(V,E) portrayed as an adjacency list, a special arc is defined as an arc (u,v) where both u and v has the same distance from source vertex s. i ...
832 views

### How to determine the time and memory complexity for solving a sliding-tile puzzle?

I have seen many posts which were related to algorithms for solving an N⨯N puzzle, but I could not figure out the time complexity or memory complexity in these algorithms, especially when we want to ...
1 vote
110 views

### Correctness of bft resulting in shortest path

I found the following proof concerning the correctness of a breadth-first traversal resulting in shortest path: source: https://people.eecs.berkeley.edu/~daw/teaching/cs170-s03/Notes/lecture6.pdf The ...
1 vote
78 views

### Proof for Queue in BFS consists of vertices of distance k and k+1

For any vertex v reachable from s, BFS computes a shortest path from s to v (no path from s to v has fewer edges). In order to prove the above proposition, The author of the book has stated that we ...
277 views

### The distinct-vertex $\alpha$-edge variant of the all-pairs shortest paths problem

The following problem is a variant of the all pairs shortest path problem: Given a weighted, directed graph $G=(V,E), |V| = n,|E| = m,$ and an integer $\alpha\ge 1$, how can I find an efficient ...
500 views

### How to find time complexity of Breadth First Search for this tree?

This is what I got from another forum, but honestly doesn't make much sense to me. Time complexity for a single tree doesn't make a lot of sense, since the function in the big O notation might be ...
1 vote
141 views

### Visiting vertices on a graph using DFS and BFS

I have this graph that I created and am wondering how DFS and BFS would work on something like this. I made this graph undirected and am going off the premise that if possible, a vertex should be ...
1 vote
297 views

### Why can't we use BFS with modifications to find shortest paths in weighted graphs

I came across this post about how we can get to all shortest paths from source (u) to destination (v) . If the algorithm is working in O(E + V), why can't we use it (after slight modifications) for ... 619 views

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 $O(|V| ... 1 vote 1 answer 104 views ### Is the first distance that gets assigned to a node in BFS always the shortest distance? Consider the following bfs pseudo code that calculates distances of all nodes from$s$in graph$G=(V,E)$. I know that if$G$was undirected and unweighted, then the above bfs would calculate correct ... -2 votes 1 answer 7k views ### Print all nodes which are the endpoint of the diameter of a tree Given a tree with n nodes, Print all nodes which are the endpoint of the diameter. 1<= n <=100000. E.g. For Above tree answer would be A,B,F,G I tried the O(n2) approach (Running Dfs from each ... 1 vote 1 answer 52 views ### Meaning of source here In graph theory, a source of a directed graph$D = (V(D), E(D))$is a vertex of it whose in-degree is zero. The book CLRS makes these statements: Given a graph$G = (V, E)$and a distinguished source ... 0 votes 1 answer 399 views ### Connectivity in Directed Graph Connectivity in undirected graph can be easily identified using Disjoint Union Set (Union Find). Is there any way to check connectivity in a directed graph efficiently other than doing Depth First ... 4 votes 2 answers 537 views ### Why do basic graph algorithms (BFS, DFS, Prim, Kruskal) have a similar structure? This is my first post on CS Stack Exchange. For some time, I have been studying basic graph algorithms, mainly BFS, DFS, minimum spanning trees and their basic algorithms (Kruskal and Prim). One thing ... 3 votes 2 answers 46 views ### There exists some number$x$so in any run of BFS from vertex$w$, so the distance from$u$to$v$in BFS tree is always$x$Studying for my finals and stuck on the following question: Prove or disprove: Given an undirected and connected graph$G=(V,E)$and three different vertices$u,v,w\in V$then there exists some ... 0 votes 3 answers 1k views ### Is DFS better than BFS for space complexity when finding path from root to a node in a tree? For simplicity, and I think without loss of generality, we can consider a binary tree. Suppose that we want to find the path between the root node and some node in the tree (we don't know where it is ... -1 votes 1 answer 170 views ### Why Breadth First Search is used for shortest path We can read on the internet: BFS finds the shortest path to the destination. But how ? Check this example: for this example we can get 40 10 20 30 60 50 70 What is ... 0 votes 0 answers 17 views ### Check if any path starting from a vertex in set A and reaching a vertex in set B is long at least k in$\Theta(G)$I am trying to verify whether it exists a path from$a \in A$to$b \in B$whose length is$\ge k$in$\Theta(G)$. This is what I have done: ... 1 vote 0 answers 27 views ### Time to form a complete graph from n vertices given that only k vertices can be used at a time [closed] I know this problem is related to the greedy algorithm and max edges incomplete graph but can't come up with a solution. Problem You are given two numbers n and k: n >= k n is the total # of ... 0 votes 1 answer 131 views ### Translating the in-order index of a node in a complete, balanced binary tree into the level-order index Consider the topmost part of a complete, balanced binary tree of all 64-bit numbers, exemplified here. As highlighted by the lack of a 7*2^64/8 term it is not ... 1 vote 1 answer 146 views ### Algorithm for finding strongest connection for a user on social network I am working on Problem 6-1 from MIT's Fall 2011 6.006 course. The problem reads as: Problem 6-1. [30 points] I Can Haz Moar Frendz? Alyssa P. Hacker is interning at RenBook (人书 / 人書 in Chinese), a ... 0 votes 2 answers 144 views ### Is the best known algorithm for the shortest path problem for an undirected and unweighted graph$O(E)$or$O(E+V)$? I'm a bit confused by Wikipedia's tables of algorithms for the shortest path problem. For an unweighted graph with$E$edges and$V$vertices, it gives the best algorithm as breadth-first search, with ... 0 votes 1 answer 125 views ### How does BFS guarantee the minimum path for this problem? https://leetcode.com/problems/bus-routes/ You are given an array routes representing bus routes where routes[i] is a bus route that the ith bus repeats forever. For ... 1 vote 1 answer 176 views ### Number of sentences and sentential forms generated by a grammar In this question, I'm considering only "finite grammars". A finite grammar can only produce a finite number of distinct sentences. The following grammar is finite in my definition: ... 0 votes 1 answer 128 views ### Shortest Path with a twist We are given a Graph G where, s ∈ V and t ∈ V. w:E such that w represents the time from u to v. We have to calculate shortest path between s to t with a twist. The twist is the turbocharger which can ... 1 vote 1 answer 57 views ### Prove$|d_{s}(u)-d_{s}(v)|\leq1$in BFS Trying to prove the following problem: Given a graph$G=(V,E)$and vertex$s\in V$, prove that:$\forall (u,v)\in E,\ |d_{s}(u)-d_{s}(v)|\leq1$where$d_s(v)$is the shortest path from$s$to$v$in ... 4 votes 2 answers 165 views ### Can Edge Belong to a cycle if it is part of multiple BFS products Given a simple connected undirected graph. with V vertices and E edges. Let e be some edge from E. If I perform |V| different BFS runs - meaning started each time from a different vertex - and in ... 0 votes 0 answers 33 views ### BFS Traversal over a graph question Starting from a random node, which of these series can be a BFS traversal (L to R)? 1 MNOPQR 2 NQMPOR 3 QMNPRO 4 QMNPOR Now, I understand that my answer (1- MNOPQR) is wrong because I got confused ... 0 votes 0 answers 256 views ### Find every path that passes through certain edges I'm faced with the following problem: Given Directed and unweighted graph, where each edge E has two attributes Goal Find every path through the 3 (or more) given edges in a specific order ... 2 votes 1 answer 445 views ### Name of BFS variant with multiple queues with different priorities Is there a name for the following variant of BFS that operates on trees with non-root starting point?: Instead of a single queue that all neighbor nodes are added to when processing a node, two ... 1 vote 1 answer 136 views ### BFS for transforming one word to another I'm having a hard time understand the reasoning in the solution of 18.7 in Elements of programming interviews (EPI): Let$s$and$t$be stings and$D$a dictionary, i.e., a set of strings. Define$s$... 0 votes 1 answer 123 views ### Minimum amount of time for two enemies to reach their destinations? Given an undirected, unweighted, and connected graph$G = (V, E)$, what is the minimum amount of time it takes for party$X$to go from$s_x$to$t_x$and party$Y$to go from$s_y$to$t_y\$? At each ... 63 views

### How to find more than 1 successive shortest paths between two vertices in unweighted and undirected graph using BFS?

I have tried to find and print more than one successive shortest paths between two vertices in the undirected graph. Using BFS as DFS will not be optimal in this case, as it can go deep into the stack....
1 vote
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### Why does this BFS solution work for this question about euclidean distance and what's its complexity?

Given a matrix of 1s and 0s where 0 represents houses and 1 represents stores, find the square of minimum Euclidean distance of every house to nearest store. Return it as a vector of vector. ...
155 views

### "Visited" vs "Seen" Positions in Breadth-First Search

I'm struggling to understand why there is such a radical difference in the execution time and number of steps required by two seemingly similar algorithms for Breadth-First Search in a 2d grid. In ...
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### Graphs which favour BFS over DFS and vice versa

I am trying to figure out what kinds of graphs are better suited to BFS and which are better suited to DFS. However i'm struggling to visualise what kind of graphs favour which search. Could someone ...