# Tagged Questions

Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

0answers
205 views

### Finding an st-path in a planar graph which is adjacent to the fewest number of faces

I am curious whether the following problems has been studied before, but wasn't able to find any papers about it: Given a planar graph G, and two vertices s and t, find an st-path $P$ which minimizes ...
0answers
313 views

### Approximate minimum-weighted tree decomposition on complete graphs

Say I have a weighted undirected complete graph $G = (V, E)$. Each edge $e = (u, v, w)$ is assigned with a positive weight $w$. I want to calculate the minimum-weighted $(d, h)$-tree-decomposition. By ...
0answers
178 views

0answers
49 views

### Closed walk in planar graphs that contains k faces

Input: Planar graph $G$ and its embedding in sphere $\Pi$, edges $e, f \in E(G)$ and integer $k$. Output: A shortest closed walk (one among possibly many, if exists) in $G$ using $e$ and $f$ which ...
0answers
122 views

### Construct matching for half of the vertices, in linear time

Suppose we have a graph $G=(V,E)$ connected and $K_{1,3}$-free. Sumner proved that every claw-free connected graph with an even number of vertices has a perfect matching (so, it is maximum matching). ...
0answers
63 views

### Multicommodity flows with minimum congestion: NP-hard?

I have a question related to a paper of Chen, Lovasz and Pak [1]. The paper concerns the construction of the Markov chain with optimal mixing time on an arbitrary graph. They prove the optimal bound (...
0answers
243 views

### Which machine learning algorithm is appropriate for predicting a vector?

I have a very large set of animal migration data, consisting of many series of vectors - each series is basically a path of a single animal. The dataset I'm using consists of 244 of these series. ...
0answers
53 views

### Heuristics to Find Circuits Allowing for Vertex Revists

I'm currently working on a project discussing applications of the Delaunay Triangulation, and the primary use-case is applications to TSP (or relaxations of the problem). See: http://www.lancaster....
0answers
102 views

### Finding partial traveling salesman path of specified length

For a given set of nodes, I can find optimal paths that visit all nodes using various traveling salesman algorithms. As a subset of this problem, I would like to be able to find shortest partial ...
0answers
40 views

### Efficient algorithms for mutual, inverse, or round-trip Personalized PageRank

I'd like to implement a similarity between two nodes (X and Y) of a graph based on a simple extension of the Personalized PageRank algorithm, either: (Mutual PageRank): the product of the PPR of Y ...
0answers
221 views

0answers
23 views

### Powerlaw graphs : Number of hubs and fraction of edges incident on them

As per the definition of power law, the fraction P(k) of nodes with k degree for large values of k , given by P(k) ~k ^-r . In this definition, the term large value is not clearly defined. Does ...
0answers
71 views

### General Steiner Tree Variants

In the general Steiner tree problem (Steiner tree in graphs), we are given an edge-weighted graph G = (V, E, w) and a subset S ⊆ V of required vertices. A Steiner tree is a tree in G that spans all ...