# Tagged Questions

Questions about graphs in which every edge is associated with a weight.

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### Faster maximum weight matching algorithm in bipartite graph

I need to do a maximum weight matching in bipartite graphs. The nodes each side are both at the level of 10^3. The graph is globally sparse while locally dense. (I don't know whether this will give ...
1answer
179 views

### When is the minimum spanning tree for a graph not unique

Given a weighted, undirected graph G: Which conditions must hold true so that there are multiple minimum spanning trees for G? I know that the MST is unique when all of the weights are distinct, but ...
1answer
67 views

### I know the algorithms, but i still don't know how to approach the questions

I study Graphs Analysis by myself and i understood most of the material just fine. But, there is one huge problem with my approach that prevents me from solving tests. I don't know how to build new ...
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34 views

### Is is possible compute the max flow with max cost through an instance of maxflow-mincost?

I have a flow network with gains. In practical terms, a gain is the opposite of a cost. So, I interested in finding the maximal gain of a network flow, what could be interpreted as finding a maximum ...
1answer
37 views

### Maximize cost in graph with variable costs

Consider the following problem. A prisoner eats once a day, he can either have a low, or a high calorie dish. In order to be allowed to eat the high calorie dish, he must not have eaten the previous ...
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44 views

### Maximum weighted antichain over a DAG with cardinality constraint

Let $G=(V,E)$ be a vertex weighted DAG (Directed Acyclic Graph), with positive real valued weights. Let also $k\leq \left\vert V\right\vert$, is there any way to find a maximum weighted antichain ...
2answers
51 views

### Equivalent definition of minimal spanning tree

Prove that $T$ is MST $\Leftrightarrow$ for any edge $uv \notin T$, $uv$ has the maximal weight on the cycle created by adding $uv$ to $T$. It's my attempt to prove $\Rightarrow$: Consider the ...
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92 views

### Optimal meeting point in directed graph

Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$. I need ...
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72 views

### Simple Way to Convert an Adjacency Matrix to a CSR Graph and Vice Versa

Let's say for the following weighted, undirected graph: I am given the adjacency matrix A[5][5]: ...
1answer
54 views

### Partial path known in Single source shortest path problem

I'm using the A* algorithm with a consistent heuristic on a graph to determine the shortest path. If the algorithm is exploring a node $p_1$ for which there is a existing knowledge about the optimal ...
1answer
43 views

### Why can't we run Bellman Ford from the source and relax edges out from the neighbours recursively and do a single pass through the edges?

At each $k$ th iteration of BF, we can are guaranteed to have computed the shortest paths that are at most $k$ long. That makes perfect sense me. If we relax a set of edges $k$ times, then we for sure ...
1answer
58 views

### Why do we have different algorithm for MST when graphs are directed?

What was the reason to come up with Chu–Liu/Edmonds' algorithm when the input graph is directed instead of using the Prim's or Krushkal's method for finding Minimum spanning tree ? What cases are not ...
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### Why does Bellman-Ford with FIFO break, if node is enqued wo/ check for duplicates?

I have implemented a variation of Bellman-Ford algorithm which uses the FIFO queue to keep track of nodes whose costs might need updating. Testing it on some random graphs with no negative weights ...
1answer
105 views

### Dijkstra's algorithm to compute shortest paths using k edges?

I am aware of using Bellman-Ford on a graph $G=(V,E)$ with no negative cycles to find the single-source single-destination shortest paths from source $s$ to target $t$ (both in $V$) using at most $k$ ...
1answer
44 views

### Edge-connectivity of a weighted undirected graph

My question consists of two parts. Let say the edge connectivity of a graph is K. I would like to change the edge connectivity value to L (> K). What is the best possible way to do so? My guess: ...
2answers
110 views

### Generate random weighted graphs representing a road network

in order to solve a DARP problem I created a Python class, that can generate random graphs. I attribute a random number to every edge which represents the cost to travel over that edge. My current ...
1answer
108 views

### What is a weighted or probabilistic automaton?

I'm developing a program that has some entities (things) that are "classified" according to "relevancy". Sort of like search engine (think PageRank). Therefore, I'm looking to implement an automaton, ...
0answers
24 views

### Branch clustering for an MST

I am working in image segmentation with super pixels. My data is a large matrix describing various attributes of each stick of pixels (such as height, width and disparity). The data comes from an ...
1answer
148 views

### All pairwise shortest paths in a graph: does knowing the path weights help?

This question concerns the all-pairs shortest paths (APSP) problem (where we are given a graph with edge $(i,j)$ given weight $w_{i,j}$ by the distances between the two nodes $i$ and $j$, and where we ...
2answers
152 views

### How to impose Euclidean distance constraint in a constraint satisfaction problem without quadratic constraints?

Best reference I could find is this one. However, I could not quite understand this one since there is no numerical example. What I am trying to achieve with one sentence How can I answer the ...
2answers
63 views

### Directed cyclic graph with node rewards and arc costs

The problem I have seems fairly simple and I feel it must have some kind of name. I have a (directed cyclic) graph. Each node has an associated reward for visiting it, and each arc costs a certain ...
0answers
158 views

### Minimum edge deletion partitioning of a planar graph

I'm interested in the time complexity of the following problem: Given an undirected planar graph $G=(V,E)$ and a weight function $w:E \rightarrow \mathbb{Z}$ (so weights can be negative, too), color ...
1answer
148 views

### Improve minimum spanning tree with new edge, with better running time than O(|V|)?

The problem gives a MST $T$ and a series of $Q$ queries, each one with a new edge $e = \{u,v\}$ such that no edge between $u$ and $v$ exists in $T$. For every query, we have to improve $T$ with $e$ ...
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96 views

1answer
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### Reweight general weighted graph to distinct graph for using Borůvka's

Is it possible to re-weight a generally-weighted graph to a distinctly-weighted graph to apply Borůvka's algorithm (wiki) for minimum spanning tree to it? I can't seem to think of a way to make a ...
1answer
48 views

### Limiting capacity of knapsack to a polynomial function of elements in the Knapsack problem

I saw somewhere that if we limit the capacity (weight) of the knapsack to a polynomial function of elements then the class of the problem changes to P, but it didn't say why. I can't figure out why is ...
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991 views

### Applications of min spanning trees

What are the significant applications of minimum spanning trees? After doing some research online and in several textbooks, I have found three real-world applications: Building a connected network. ...
1answer
66 views

### Choice of algorithm for hierarchical clustering for minimizing network communication costs

Suppose I have a large distributed task running on a cluster system where part of the workload is compute bound and part depends on network performance. Data transfer is not completely homogeneous ...