# Tagged Questions

a mathematical structure that contains a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices

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### Connected components of undirected graph

Suppose I have an undirected graph G with vertices v1...vn and edges. Right now it is in adjacency list representation. For every time moment I have as input some subset of vertices that are "active" ...
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### Codeforces : 505C. Mr. Kitayuta, the Treasure Hunter

Question : Is the attached logic correct? I am asking since my code based on this logic failed. Here is the problem link. Reproducing here verbatim : The Shuseki Islands are an archipelago of ...
614 views

### Is there some structured format for drawing source control branching diagrams?

Everyone on my team draws branch diagrams differently, including how branches exit or reintegrate to the parent, how cherry-pick merges are shown, and a host of other aesthetic choices. Is there some ...
294 views

### Why does this algorithm work in O(n m)?

This is from a blog post on Codeforces. I couldn't really understand why the editorialist goes on to claim that this code works in O(n m) This is a graph problem, where we are supposed to find the ...
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### Why does this implementation of Dijkstra's algorithm work in O(n^2)?

Here is the code I use for implementing Dijkstra's algorithm. Consider a graph with n vertices and m edges. Shouldn't it run in O(n^2 m) ? Someone may say that there are n vertices and each edge gets ...
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### Mathematically correct A* heuristic / distance estimator for a latitude / longitude graph

I have a graph in which each node is a geographical point on the surface of the earth, defined by it's latitude / longitude coordinates. Correct ways to calculate the distance between two such points ...
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### Setting and getting values from a x-y graph

I have a bunch of x-y graphs given to me and I need to be able to transform them into some kind of data structure from which I will be able to get Y with X value. The problem is, though that I have 4, ...
335 views

### What is the minimum cost graph inside a strongly connected component, which connects every vertex?

So for MST there are 2 possible definitions in an undirected graph. Keep in mind that in an undirected graph the MST algorithm always has n - 1 edges and no cycles. In an undirected graph, it doesn't ...
386 views

### Merge directed acyclic graphs minimizing number of nodes

I have some DAGs (directed acylic graphs) and I want to merge them in order to minimize the number of nodes (we could say that every node has a cost, while edges are free). These four different DAGs (...
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### How do you unit-test code using graphs?

I am writing (recursive) code that is navigating a dependency graph looks for cycles or contradictions in the dependencies. However, I am not sure how to approach unit testing this. The problem is ...
415 views

### Finding shortest path between nodes with a twist

Note: if you feel that I should include code, please tell me. I am solving a problem of finding shortest path between nodes. I am given the vertices between nodes, however they are one sided (ie you ...
268 views

### Find 'Connected Components' in undirected, unweighted graph coded as a 2d array

Given an undirected, unweighted graph coded as a 2d array, how can I find the number of different connected components? Example There is the following 2d array (I'm not putting any brackets to ...
374 views

### Number of sequences when no adjacent items can be the same

I came across this one problem, There is a particular sequence only uses the numbers 1, 2, 3, 4 and no two adjacent numbers are the same. Write a program that given n1 1s, n2 2s, n3 3s, n4 4s ...
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### Shortest Path Between Two Nodes in a +10 Million Nodes Graph

I have my own knowledge graph representation, read from ConceptNet and NELL, containing tens of millions of nodes in which I want to calculate the nearest distance (if any) between two concept nodes. ...
479 views

### Data structures and algorithms for a directed rooted tree with inherited properties?

I need to represent a directed rooted tree in memory. The caveat is, that nodes have properties. And those properties are inherited (but not 100%) by the child nodes, recursively. What would be a ...
320 views

### Find n nodes farthest away from each other

I'm looking for an algorithm that gives me the n nodes that are the farthest away from each other. Can this be accomplished relatively efficiently? To clarify my question: I think of the problem as ...
539 views

### How can I find the shortest path between two subgraphs of a larger graph?

I'm working with a weighted, undirected multigraph (loops not permitted; most node connections have multiplicity 1; a few node connections have multiplicity 2). I need to find the shortest path ...
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### Finding the shortest path through a digraph that visits all nodes

I am trying to find the shortest possible path that visits every node through a graph (a node may be visited more than once, the solution may pick any node as the starting node.). The graph is ...
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### How to represent a graph with multiple edges allowed between nodes and edges that can selectively disappear

I'm trying to figure out what sort of data structure to use for modeling some hypothetical, idealized network usage. In my scenario, a number of users who are hostile to each other are all trying to ...
176 views

### City exploration algorithm

The purpose of the algorithm is to create n routes on a geographical map, where n is being given, whereas all routes take no longer than t time units by foot and end where they start, while trying to ...
109 views

### Which approach would be better for persisting these overridable configuration keys and values? A simple key-value store, or a graph database?

I'm creating a system where there are config keys and values. So for example: config.key = 10 Is an example of a configuration key and a value. These keys can also have overrides based on "...
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### Equidistant polygons

Consider these polygons: For reasons of simplicity I only consider triangles or polygons with 4 vertices. These shapes are specified by the vertices, the output of the program should be modified ...
528 views

### An algorithm for finding converse duplicates of ordered pairs

Given an array of ordered pairs of values, what algorithm will find converse duplicates? [Converse meaning the same values, but in the opposite order.] That is, given [ab,ac,ad,bc,bd,ca,db] is there ...
871 views

### Understanding Tarjan's Bridge-finding algorithm

Tarjan's algorithm for finding bridges in a graph is found here: http://en.wikipedia.org/wiki/Bridge_(graph_theory)#Tarjan.27s_Bridge-finding_algorithm. However, I don't understand the condition for ...
173 views

### Matching weighted unbalanced Bipartite graph

I am looking for a way to solve an assignment problem, but I am having some problems finding the correct algorithm to use. I have 2 list of nodes A and B, and in my problem may the length of A not be ...
387 views

### Improving the running time of Breadth First Search and Adjacency List creation

We are given an array of integers where all elements are between 0-9. have to start from the 1st position and reach end in minimum no of moves such that we can from an index i move 1 position back and ...
147 views

### How to canonise a road network

I am working on geographical data which represents the road network of some city and I need to automatically fix inaccuracies in the data. Data was manually produced by “drawing” the road network ...
253 views

### Maze generation given intersection tree

Background Information: I'm building a 2D maze generator. I have tried Prim's algorithm, Wilson's algorithm, and a recursive backtracker algorithm for generating my maze, however was not satisfied ...
348 views

### Euclidean Space Fully Connected Nondirectional Graph: Shortest Path to all nodes

So this may be a question that is born of my inability to properly express my intentions to Google. In a fully connected non-directional graph such that any three points can be properly represented ...
512 views

### How to find number of points with same minimal distances on matrix

I'm trying to find the number of points in a matrix with the same minimal distances. Start with a MxN matrix, where M and N < 50000. There is given a set of fixed points, with their respective ...
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### Heuristic Approach for Flexible DIFF Implementation

I have created a DIFF implementation to compare document revisions at work. It is based on An O(ND) Difference Algorithm and Its Variations. One thing that has become important is to take the list ...
1k views

### Finding most Important Node(s) in a Directed Graph

I have a large (≈ 20 million nodes) directed Graph with in-edges & out-edges. I want to figure out which parts of of the graph deserve the most attention. Often most of the graph is boring, or at ...
298 views

### Question on Graph

I am trying to implement a graph data structure in C#. I have the following interfaces: public interface IVertex<TValue> { TValue Value { get;} VertexList<IVertex<TValue&...
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### Algorithm for defragmenting cross-pipe issues in a network for routing signals through?

I have a network I'm responsible for routing signals through. You can think of the network as a directed graph of nodes (hardware) but each edge is really a pipe capable of fitting a specific ...
157 views

### What algorithm should I use to find the shortest path in this graph

I have a problem about the calculation of shortest paths on an unweighted and undirected graph. Which algorithm I use to calculate the shortest path between a node A and node B that passing through a ...
451 views

### Weight-maximizing (weighted vertices) path algorithm

I am looking for description (name of algorithm, code, pseudocode, etc.) that can help me frame this problem and find the appropriate recursion and the most efficient solution. Problem: Given a ...
961 views

### What graph traversal algorithm should I use?

I would like to write an algorithm which can traverse a graph and hopefully later I can implement it to use for an indoor navigation system. The graph would come from floor plans of a building and ...
974 views

### Optimal “if-else” tree algorithm to minimize duplicate code

I'm having trouble formulating this problem as an algorithm: I have a set of conditionals (combined with &&) and operations, for example: if (A && B) execute C else if (D &&...
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### Representation of time expanded graph

I want to build a time expanded graph with time discretization Dt that starts at t = 0 and ends at t = T where between the node (n1, t) and the node (n2, t') is an arc if and only if (n1, n2) were ...
84 views

### using internal or external iterators over graph edges

I've written some code to manipulate sparse graphs for school work I'm doing, and I have an operation which requires me to loop over all the edges of a graph. The interface I need to implement is some ...
370 views

### How to solve binary labeling with graph cut?

Many literature references suggest that the binary labeling problem can be converted into a graph cut problem and solved with the max flow/min cut algorithm. I'm trying to understand the formulation ...
172 views

### How can I find all connections in a mesh network/graph?

Suppose I have a mesh of relationships, such as Friends who trust some friends and not others A IPv6 router that needs to locate peers across the Internet A PGP Web Of Trust that needs two people ...
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I thought I was doing breadth-first graph search correctly, but my instructor's grading script is telling me that my answer is incorrect. From the instructions: Consider a breadth-first graph ...
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### Storing a drawn graph information in database for web application

Well while developing a web application that allow users to draw graphs (flow charts, ER diagram , UML, .... etc) the information of drawn items and their relation to each other and position on canvas ...
701 views

### Is it possible to represent mutation of object-graph efficiently with immutable states?

I am practicing using of immutable object in C++. My personal goal is representing generic object graph (in heap) with sequence of immutable graphs. Building the multi-version graph itself isn't that ...
214 views

### Class instance clustering in object reference graph for multi-entries serialization

My question is on the best way to cluster a graph of class instances around specifically marked objects (objects are the graph nodes and the references to each other are the directed edges of the ...
951 views

### Connected components of a graph using Prolog

Given a corner x of an undirected Graph G I would like to ask for the connected component of x, but my first try does not work as desired. Here it is: edge( a,b ). edge( b,a ). edge( b,c ). edge( c,...
237 views

### Algorithm in undirected BFS graph

I'm trying to put together an algorithm that will display the node degree for every node in a breadth first tree graph (assume BFS was called). Assume it's an undirected graph. I'm not sure how to ...