When adding a random edge to a graph, which bridge edges are not bridge edges any longer?
algorithm,graph,graph-algorithm
If you allow preprocessing, there is a fast method: Construct the bridge-block forest, whose vertices are 2-connected components, and whose edges are bridges. (It's a tree if the graph is connected.) When you add an edge, if this connects points in the same 2-connected component, nothing happens. If you connect...
Best graph algorithm for least transfer in an electric grid
Your problem is easily reduced to a well-known minimum-cost flow problem: The minimum-cost flow problem (MCFP) is to find the cheapest possible way of sending a certain amount of flow through a flow network. This reduction can be done the following way. Add a dummy "source" and "sink" vertices to...
Shortest paths with 2 constraints (Weight and Colour)
algorithm,graph,graph-theory,graph-algorithm,dijkstra
I think your approaches are actually equivalent, provided that for approach #1, you record only the shortest distance to each node for each number of red edges used -- you don't need to record the entire path (just as you don't need to record it for ordinary Dijkstra on an...
Find the path with minimum cost between multiple nodes
javascript,angularjs,graph-algorithm
It is called Hamilton cycle problem. Or travelling salesman problem. https://en.wikipedia.org/wiki/Travelling_salesman_problem...
graph traversal - finding 2 shortest paths for 2 entities such they are never in contact (both at the same node)
algorithm,graph-theory,graph-algorithm,shortest-path
I think you might consider a dynamic programming approach. At iteration 0, let s_0 = {(origin_0, origin_1)}. For iteration k+1, let s_k+1 = {(x,y) | x != y, exists an (prev_x, prev_y) in s_k s.t. e(prev_x, x) in E and e(prev_y, y) in E}. This should proceed forward with |s|...
Find separated lines in a 2D coordinate system
c#,algorithm,swift,coordinates,graph-algorithm
Here is an example I come up with: (tested in a Playground with Swift 2 Xcode 7 beta 2) struct Point{ var x, y: Int init(_ x: Int, _ y: Int) { self.x = x self.y = y } /** get points around it (Xs around P) if all {...
How to efficiently update such a directed graph?
You can have each node maintain a list of dependent nodes and also a "dirty" flag. Then whenever a node changes, recursively set the dirty flag on every dependent node. (If a node is already marked dirty, don't recurse.) You can then make a second pass to re-evaluate each dirty...
How to apply Dijktra algorithm on this graph?
You apply the Dijkstra algorithm the normal way and the shortest path from a to c is really 3. However, you should read the pseudocode for Dijkstra to understand that table. Firstly, Dijkstra returns an array (or another data structure, depending on implementation, for our purposes just say it's an...
Detecting cycles in an oriented dependency graph and detecting if a vertex is part of the cycle or just depending on one
algorithm,language-agnostic,graph-algorithm
Tarjan algorithm for searching strongly connected components of a directed graph http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm allows you to make the distinction you need.
Represent walls in a adjacency list
algorithm,graph,artificial-intelligence,graph-algorithm,maze
Well, it is hard to say anything for sure without knowing more details, but for most of the shortest path search algorithms it is fine not to create any nodes for cells that contain a wall at all.
How I can represent a graph in java? [closed]
java,algorithm,graph,graph-algorithm
You can also use adjancy list using the following code snippet - int n; List<Integer>[] adj; AdjacencyLists(int n0) { n = n0; adj = (List<Integer>[])new List[n]; for (int i = 0; i < n; i++) adj[i] = new ArrayStack<Integer>(Integer.class); } Then add edge using the function - void addEdge(int i,...
To print the boundary of Binary Tree
algorithm,tree,binary-tree,binary-search-tree,graph-algorithm
I guess this should do the trick: traverse(BinaryTree *root) { if (!root) return; cout << p->data << " "; if (root->left ) traverseL(root->left ); //special function for outer left if (root->right) traverseR(root->right); //special function for outer right } traverseL(BinaryTree *p) { cout << p->data << " "; if (root->left )...
Java: Uniform Cost Search with Node class
java,graph-algorithm,priority-queue,comparable
To satisfy the sorting capability of the PriorityQueue class (used by UniformCostSearch), your Node class must implement the Comparable interface, not the Comparator interface. To use the node parent in your comparison, you might try this: @Override public int compareTo(Node that) { if (this.parent != null && that.parent != null)...
Query ArangoDB general-graph for common neighbors with more than 2 start vertices?
graph,graph-algorithm,arangodb
You can simply pass the same set of vertices as both parameters for common neighbors. Then repack the result in a better format for AQL to compute the intersection: let res = ( let nodes = ["a/A","a/B","a/C"] for n in GRAPH_COMMON_NEIGHBORS("g",nodes , nodes) for f in VALUES(n) return VALUES(f) )...
Codeforces #236 Div2
That's a somewhat muddled editorial. Let's focus on creating 0-interesting graphs first. The key fact from graph theory is the following formula. sum_{vertices v} degree(v) = 2 #edges In a graph where every vertex has degree 4 (4-regular graph), the left-hand side is 4n, so the number of edges is...
Sampling a Large Undirected Graph
algorithm,social-networking,graph-algorithm,sampling,directed-graph
You can treat the undirected graph like a directed graph for the purposes of sampling. Any sampling strategy for a directed graph should work assuming it allows cycles. You simply want to sample the nodes and edges, so any edges that become part of the sample just accept the edge...
Detecting connectedness of nodes over a long time in a graph
There are ways to solve this problem fully online, but they're more complicated than this answer. The algorithm that I'm proposing is to maintain a spanning forest of the available edges, together with the number of components of the spanning forest (and hence the graph). If we were attacking this...
Shortest paths that are impossible for BFS to find?
algorithm,search,graph-theory,graph-algorithm,breadth-first-search
The Example Let G = (V,E) a graph with V = ℕ ∪ {-1, 0} and E = { {-1,t}, {t,0} | t ∈ ℕ } and let s = -1 and f = 0. There exist an infinite number of paths of length 2 from s to f, but...
Proving breadth-first traversal on graphs
algorithm,graph-algorithm,discrete-mathematics,proof
Disclaimer: I don't know how much formal you want your proof to be and I'm not familiar with formal proofs. induction on the while loop: Is it true at the beginning? Does it remain true after a step (quite simple path property)? same idea, induction on k (why k+1???): Is...
Find if there is a non-simple path from v to t on a directed graph
algorithm,graph,computer-science,graph-algorithm,dfs
Step 0: If there is no path from v to t, then answer is NO. Step 1: Make the graph G' after collapsing all the strongly connected components of G. Step 2: If the vertex 'v' is a part of some SCC consisting of more than 1 vertex, then there...
Partially coloring a graph with 1 color
algorithm,graph,graph-algorithm
This problem is NP-Hard as well, and is known as maximum independent set problem. A set S<=V is said to be Independent Set in a graph if for each two vertices u,v in S, there is no edge (u,v). The maximum size of S (which is the number you are...
Minimal spanning tree with degree constraint
algorithm,graph,graph-algorithm,minimum-spanning-tree,degrees
To summarize the suggested algorithm [with tightened requirements on epsilon (which you called x)]: Pick a tiny epsilon (such that epsilon * deg(u) is less than d, the smallest non-zero weight difference between any pair of subgraphs). In the case all the original weights are natural numbers, epsilon = 1/(deg(u)+1)...
Graph Theory - Length of Cycle UnDirected Graph - Adjacency Matrix
algorithm,graph,graph-algorithm
Given the conditions in the question (that is, the only edges in the graph are part of the cycle), the length of the cycle is the number edges in the graph, which is half the number of 1s in the adjacency matrix (each edge (i, j) appears twice in the...
Finding the largest subsets of nodes in a tree subject to some constraints?
tree,binary-search-tree,graph-algorithm,depth-first-search,breadth-first-search
The problem you're trying to solve is called the maximum independent set problem applied to trees. As a hint, think about the following: For each complete subtree of the tree, think about the optimal solution for that subtree in two cases - the case where you include that node in...
Algorithm For Vertex Removal From Tree
algorithm,tree,graph-algorithm
Create a recursive function that does a post-order traversal of the tree. The function returns the subtree size and a vertex, or the vertex can be global (in which case you just set it instead of returning it). Call the function for the root. Call the function on each child's...
Check root node cut JAVA
java,algorithm,graph,graph-algorithm
You may just need this test: boolean isCutRoot(Vertex root) { final Edge[] rootEdges = graph.incidentEdges(root); return rootEdges != null && rootEdges.length >= 2; } However, if it is possible for multiple edges from the root to point to the same vertex, you need to modify the above method to check...
Flawed logic in A* implementation
java,algorithm,code-review,graph-algorithm,path-finding
First of all, you are mostly on track. I strongly suspect the code you posted is still under development and has some problems. But, still your assumption of distance is positive is not correct in general. A* is a graph search algorithm and edges can have negative weights as well...
Disconnecting a connected graph
algorithm,graph,graph-algorithm
You can use a maximum flow algorithm to compute the minimum cut between A and B in your graph. Runtime: O(n*m) with an excess-scaling push-relabel variant (since you have only unit capacities). Your solution is O(2^m * (n + m)) if you use DFS or BFS for reachability in the...
Can a non-oriented graph have more than one Eulerian cycle?
The cycle is called Eulerian, iff it contains all edges, exactly one time each. That means that Eulerian cycles can only differ by edge's order (I propose to exclude edge's cyclical permutations as trivial option). It is possible to find Eulerian cycle, using Fleury's algorithm: in short, move as you...
How to use heaps with dictionaries to implement single source shortest path algorithm?
python,algorithm,dictionary,graph-algorithm,dijkstra
You can still use a heap even if it requires a list. graph.keys() returns a list of keys in your dictionary. The heap can then be built using the keys and if you need to find vertexes, dictionary lookup can be used. vertexes = graph[heap.pop()]....
Reduction from 3-Coloring to Fair-3-Coloring
They don't have to be connected. Just throw in some loose nodes. Those nodes are just there to fix the number of colours, they shouldn't be affecting colourability. You have to add more than just 1 or 2 (which would be enough to get a multiple of 3) in general....
Should D. B. Johnson's “elementary circuits” algorithm produce distinct results?
algorithm,graph,go,graph-theory,graph-algorithm
The redundant permutations are filtered out because the start node of each returned permutation is always less than all the remaining elements (under some ordering). I suspect the problem is in a missing implementation of these steps: AK:= adjacency structure of strong component K with least vertex in subgraph of...
Undirected, weighted graph partitioning
algorithm,language-agnostic,graph-algorithm
What you are looking for is called the minimum cut of a graph. By the Max-flow_min-cut_theorem the value of the minimum cut is equal the the value of the maximum flow. Computing the maximum flow in a network is a standard problem and there are several algorithms for computing this...
Wraping of equispaced point set in a given direction
java,r,algorithm,geospatial,graph-algorithm
I would do it like this: may be some 2d array point grouping to match the grid that should speed up all the following operations. compute average grid sizes (img1 from left) as two vectors create blue points (img2) as: gray_point (+/-) 0.5*blue_vector create red points (img3) as: blue_point (+/-)...
Heuristic to find the maximum weight independent set in an arbritary graph
algorithm,graph,graph-algorithm,linear-programming,np-complete
It's possible to formulate this as the following problem. Suppose each vertex v in the graph has weight w(v). You define a variable x(v), and use some out-of-the-box linear programming solver to solve max \sum_v w(v) x(v) (maximize the weight of chosen vertices) subject to x(u) + x(v) <= 1,...
Find shortest path between two nodes in directed weighted graph
algorithm,graph,computer-science,graph-algorithm,shortest-path
Edited my answer based on counter example by David Eisenstat. The example you give in your question is not a good example of when Dijkstra will not work. I believe you can do this by modifying Dijkstra. The key is to keep track of multiple alternatives for each Vertex. Not...
Graph algorithm to collect all edges which are on any path between two nodes
algorithm,graph,graph-algorithm
To get an overall result I'll report what I did. I implemented the in the question mentioned algorithm. (Lets call it thigg's algorithm, because noone mentioned a name) Thigg's algorithm: for each node in the graph: if there is a path from src to this node and a path from...
Getting a DFS from a BFS?
algorithm,search,data-structures,graph-algorithm
If you take a classic BFS algorithm and replace the FIFO queue with a LIFO stack, you will indeed get DFS vertex discovery order - so called DFS pre-ordering. I.e. the order in which your algorithm will visit graph vertices for the very first time will be exactly the same...
Efficiently build a graph of words with given Hamming distance
python,algorithm,graph-algorithm,hamming-distance
Assuming you store your dictionary in a set(), so that lookup is O(1) in the average (worst case O(n)). You can generate all the valid words at hamming distance 1 from a word: >>> def neighbours(word): ... for j in range(len(word)): ... for d in string.ascii_lowercase: ... word1 = ''.join(d...
Algorithm to arrange randomly sized rectangle images with optimally maximum spacing between them
algorithm,random,graph-algorithm,overlap
Here is the description of an algorithm that finds an optimal envelop for image sprites. You can easily bound it to your container side. Then as per my comment: find all the center points of your rectangles, and enlarge those points from the middle of the container by a ratio...
Datastructure related. Find all arrays elements greater than or equal to given input
java,algorithm,data-structures,graph-algorithm
The approach that comes to mind could be to keep an ordered list of the orders and perform a binary search for the limit amount. All orders before that point in the ordered list will be less than the limit amount. // Generate a random array of numbers Random r...
is bellman-ford can be done in a single iteration?
algorithm,graph-algorithm,bellman-ford
Sort a shortest path tree topologically.
Modified shortest path algorithm - vertices have points
algorithm,graph,graph-algorithm
So after this experience, I found that you should look into the ant colony algorithm and apply it to the traveling salesman problem. You could alternatively use a modified greedy algorithm approach that starts at a random point and chooses the next location based on a random sided die based...
Computing Min-Cut of a Graph with No Reverse Edges
algorithm,graph,graph-algorithm,flow,edge
I believe this should work: For every edge, add a reverse edge with infinite capacity. That way if the min-cut is finite, original edges can only go from S to T, not the other way round.
Finding a minimal tree-type network of a graph where each node is connected to each other and find the sum of each node to all the other nodes
algorithm,tree,graph-theory,graph-algorithm
There are 13^11 ~ 1.8e12 spanning trees on 13 nodes, so brute force is out of the question. I believe that the intended solution is dynamic programming. For each pair comprised of a nonempty subset of nodes and a distinguished node belonging to the subset (the root), compute the optimal...
Iterative version of the Bron–Kerbosch algorithm?
algorithm,graph-algorithm,pseudocode
The recursive version is given in Wikipedia as this: BronKerbosch1(R, P, X): if P and X are both empty: report R as a maximal clique for each vertex v in P: BronKerbosch1(R ⋃ {v}, P ⋂ N(v), X ⋂ N(v)) P := P \ {v} X := X ⋃ {v}...
Maximum weighted pairing algorithm for complete graph
algorithm,graph-algorithm,matching,scilab
I do not know Scilab I am afraid, but if you are willing to use Python it is very easy as the Networkx library provides support for this function: import networkx as nx import networkx.algorithms.matching as matching def C(i,j): return i*j n=40 G=nx.Graph() for i in range(n): for j in...
Finding the number of edges and performing a topo sort in my graph implementation
c++,graph,graph-algorithm,topological-sort
First, for the number of edges, it would be simpler to count them directly when you build the graph (just add a counter in your Digraph class and increment it each time you add an edge … ) For the topological sort, first I have a question: your edges are...
Algorithm for coloring a hexagon tile map with minimum distance (3) for reoccurring colors
algorithm,graph-algorithm,tile,hexagonal-tiles
Let's set up a coordinate system where the hex with coordinates (i,j) is adjacent to (i-1,j), (i-1,j+1), (i,j-1), (i,j+1), (i+1,j-1), (i+1,j). (0,3) (2,2) (4,1) (1,2) (3,1) (0,2) (2,1) (4,0) (1,1) (3,0) (0,1) (2,0) (1,0) (0,0) I'm going to apply a shear transform so that I can draw hex grids compactly...
Betweenness centrality Brandes algorithm
algorithm,graph,graph-algorithm
The Brandes' algorithm gives the exact centrality of each vertex. I don't know which implementation of the algorithm is used in Sage, but chances are that it's a precision problem. The accumulation part of the algorithm is probably the trickiest. When you reach that part, you have in sigma...
Graph with colored edges: shortest paths with at most k color changes?
algorithm,graph,time-complexity,graph-algorithm,shortest-path
This can be solved in time O(nm + n2 log n) by running Dijkstra's algorithm on an appropriately-constructed graph. To motivate the intuition for where we're going, let's assume for now that the optimal path makes at most one color change and starts by following a red edge. The path...
What's the difference between the minimum spanning tree algorithm for undirected vs directed graphs?
algorithm,graph,tree,graph-algorithm
The core of your question seems to be what makes finding an MST (technically called an optimum branching or minimum-cost arborescence) in a directed graph different and therefore harder than finding an MST in an undirected graph. Both Prim's and Kruskal's algorithms work because of the cut property. If G...
Is there a way to find if path exists in a Directed acyclic graph in constant time (O(1))?
algorithm,graph,graph-algorithm,directed-acyclic-graphs
Let's assume that f(i, j) is the number of paths from i to j vertex. Initially(I assume that the graph is empty, if it is not the case you can add all edges using the add operation) f(i, j) = 1 if i = j and 0 otherwise. To add...
Generate states for depth first search
java,algorithm,graph,graph-algorithm,depth-first-search
Switch 4 : Toggles all numbers that have modulus 1 with 3 1 % 3 = 1 4 % 3 = 1 7 % 3 = 1 10 % 3 = 1 Switch #1: 0000000000 <- Switch #2: 0101010101 <- Switch #3: 1010101010 Switch #4: 0110110110 <-...
How to design an O(m) time algorithm to compute the shortest cycle of G(undirected unweighted graph) that contains s?
You can run a BFS from your node s as starting point, this will give you a BFS-tree. Afterwards you can built a lowest-common-ancestor (LCA) data structure on this BFS-tree. This can be done for example with Tarjan's lowest-common-ancestor algorithm. I will not got into details here. Given two nodes...
Python: Comparison between list items that isn't redundant
python,for-loop,optimization,comparison,graph-algorithm
You can iterate through pairs using itertools.combinations for pair in itertools.combinations(d['people'], 2): first, second = pair if first[0] == second[0]: g.connectThem(first, second) These are the pairs that are produced from combinations [('John', 'Carry'), ('John', 'Joe'), ('John', 'Greg'), ('John', 'Carl'), ('John', 'Gene'), ('Carry', 'Joe'), ('Carry', 'Greg'), ('Carry', 'Carl'), ('Carry', 'Gene'), ('Joe',...
applying a function to graph data using mapReduceTriplets in spark and graphx
scala,network-programming,apache-spark,graph-algorithm,spark-graphx
I think you want to use GraphOps.collectNeighbors instead of either mapReduceTriplets or aggregateMessages. collectNeighbors will give you an RDD with, for every VertexId in your graph, the connected nodes as an array. Just reduce the Array based on your needs. Something like: val countsRdd = graph.collectNeighbors(EdgeDirection.Either) .join(graph.vertices) .map{ case (vid,t)...
Detect cycle in a graph using Kruskal's algorithm
c++,algorithm,graph-algorithm,disjoint-sets,union-find
MAKE-SET(v) means that you're initializing a set consisting of only the vertex v. Initially, each vertex is in a set on its own. FIND-SET(u) is a function that tells you which set a vertex belongs to. It must return a pointer or an ID number that uniquely identifies the set....
depth first search algorithm working
java,data-structures,tree,graph-algorithm,depth-first-search
You don't need stack here. Only recursion: public void dfs(Node node) { if (node == null) { return; } System.out.println("Node: " + node.getVertex()); node.state = State.Visited; for (Node n : node.getAdjacent()) { if (n.state != State.Visited) { dfs(n); } } } UPDATE To check path existence: public boolean isPath(Graph graph,...
Pairs of Vertices Unreachable from Each Other in a Directed Graph
algorithm,time-complexity,graph-algorithm
If you can find all strongly connected components in the linear O(V + E) time requested then you are done. This may seem a bit overkill but it solves the problem. To find all strongly connected components, assuming your graph is represented as an adjacency list, perhaps the simplest O(V...
Algorithm like Bellman-Ford, only for multiple start, single destination?
algorithm,graph,graph-algorithm,path-finding,bellman-ford
Just reverse all the edges, and treated destination as start node. Problem solved.
Number of unique sequences of 3 digits (-1,0,1) given a length that matches a sum
algorithm,math,graph-algorithm
You can use a dynamic programming approach. The sketch of a recurrence is: M(0, 1) = 1 M(t, n) = T(t-1, n-1) + T(t-1, n) + T(t-1, n+1) Of course you have to consider the border cases (like going off the board or not allowing to exit the end of...
Can Bellman-Ford algorithm be used to find shorthest path on a graph with only positive edges?
algorithm,graph-algorithm,dijkstra,bellman-ford
Yes, it will give the same results. It will run slower, though, as it could also have been used for graphs with negative edges (subject to the absence of negative cycles). If you look at the proof of BF's correctness, there is no assumption there that some of the edges...
Find linearity in a graph
c,algorithm,graph,graph-algorithm
Do you mean constant or linear? If you mean linear: Why not take the differences of adjacent values and search for a sequence that stays close to constant? If you mean constant: Why not take the differences of adjacent values and search for a sequence that stays close to 0?
Finding the smallest number of steps between two points?
java,vb.net,algorithm,graph-algorithm
For your problem, I think BFS still works. Using BFS to solve traditional Maze problem, starting from the beginning point, you have to: 1. Enqueue every point that is accessible (not a piece of wall, and not visited) and connected to the current point. 2. Dequeue current point and mark...
PageRank toy example fails to converge
python,web-crawler,graph-algorithm,pagerank
It was the edge adding function that ruined it all. Fixed it to: def update_graph_links(): """register each node with neighbours pointing at it""" global pr_nodes for node in pr_nodes.itervalues(): for u in node.links_to_node: if u in pr_nodes: pr_nodes[u].links_from_node.add(node.url) return After a few adjustments, some refactoring and adding proper comments it...
Maximum weighted independent set in bipartite graph
algorithm,graph-algorithm,independent-set
In any graph, the complement of an independent set is a vertex cover and vice versa, so your problem is equivalent to finding the minimum weight vertex cover in the graph. The latter can be solved using maximum flow techniques: Introduce a super-source S and a super-sink T. connect the...
What data structure or design pattern to use to map a defined sequence of steps
java,oop,design-patterns,graph-algorithm
It does feel a bit like a flavor question. If I understand correctly you have data driven flow , by which I mean you have some data (in this case in form of xml's and scripts) that dictates what actions will be taken (so it's not known at compile time,...
Approximation Algorithm for non-intersecting paths in a grid
algorithm,graph-algorithm,approximation
Here's a program written in Python that walks all potential paths. It uses recursion and backtracking to find the paths, and it marks a grid to see which locations are already being used. One key optimization is that it marks the start and end points on the grid (10 of...
How to compare communities in two consecutive graphs
Actually this is not an easy question. In general you need to match the communities in the two graphs, using some rule or criteria that the matching optimizes. As you can have different number of communities, the matching is not necessarily bijective. There were several methods and quantities proposed for...
How to start Dijkstra's algorithm on a graph stored in a dictionary
python,algorithm,dictionary,graph-algorithm,dijkstra
Dijkstra's algorithm solves the single-source shortest-path problem. Given a graph and a vertex in the graph, it finds the shortest path to every other vertex. If you want your implementation to run fast, you must use a priority queue. It's fine to use a dictionary to represent the graph initially,...
Compute costs only of paths between all pairs in weighted graph
No, there is no algorithm better then O(n2). The algorithm will need to at least go over each pair. There are O(n2) possible pairs in the graph: . Therefore the algorithm bottom boundary is = O(n2)....
Algorithm for finding the path that minimizes the maximum weight between two nodes
algorithm,graph,graph-algorithm,shortest-path
Here is a simple solution: Sort the edges by their weights. Start adding them one by one(from the lightest to the heaviest) until X and Y become connected. To check if they are connected, you can use a union-find data structure. The time complexity is O(E log E). A proof...
Find a shortest path with some conditions
algorithm,graph,graph-algorithm
Here is a faster solution: Let's find paths that contain the smallest number of black cells. We can use 0-1 breadth-first search. An edge that leads to a white cell should have a weight 0 and an edge that leads to a black cell should have a weight 1. There...
Find a MST in O(V+E) Time in a Graph
algorithm,graph,graph-algorithm,minimum-spanning-tree
I would suggest you to do something like the second answer in the given question: This is prim's algorithm : Start by picking any vertex to be the root of the tree. While the tree does not contain all vertices in the graph find shortest edge leaving the tree and...
Algorithm to find k neighbors in a certain range?
algorithm,data-structures,graph-algorithm,nearest-neighbor,point-clouds
Your problem is part of the topic of Nearest Neighbor Search, or more precisely, k-Nearest Neighbor Search. The answer to your question depends on the data structure you are using to store the points. If you use R-trees or variants like R*-trees, and you are doing multiple searches on your...
How to store a Euler graph struct?
algorithm,graph,graph-algorithm
You can use an adjacency matrix to store graphs with multi-edges. You just let the value of c[i][j] be the number of times that vertex i is adjacent to vertex j. In your first case, it's 1, in your second case, it's 3. See also Wikipedia -- adjacency matrices aren't...
Finding best paths in a fully connected graph
algorithm,graph,graph-algorithm
The problem you're describing ends up being NP-hard (via a reduction from the longest path problem), so unless P = NP there aren't going to be any algorithms that are correct on all inputs and efficient on all inputs. You'll either need to be willing to accept answers that aren't...
A Dynamic Programming or Graph Algorithm, a Nice Questions
algorithm,math,graph,dynamic-programming,graph-algorithm
To my understanding, the problem can be solved as a Maximum Bipartite Matching, however the modelling requires the graph to be relatively large compared to the original input; for every feasible edge (s_i,b_j) introduce s_i nodes for the producer partition and b_j for the consumer partition and connect each producer...
Decompose a network into components with equal number of vertices
r,algorithm,graph,network-programming,graph-algorithm
Given the set Sn of all n-tuples of connected node subsets, construct the set of all n+1-tuples of connected node subsets by iterating over all s={a1,a2,...an} and there iterating over all ai to find a connected node ax which isn't in s. Build s'={a1,a2,...an,ax} and add to Sn+1 (which, as...