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# Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

216 questions with no upvoted or accepted answers
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977 views

### Counting Isomorphism Types of Graphs

Polya's counting theorem leads to an algorithm for counting (precisely) the number of isomorphism types of graphs with $n$ vertices in $\exp (\sqrt n )$ steps. From Polya theorem you get a formula ...
572 views

### Complexity of finding the smallest well-covered completion

This is related to an earlier question on which graphs have the property that all maximal independent sets are maximum — such graphs turn out to be known as the well-covered graphs. Any graph $G$ is ...
296 views

189 views

### what is the best heuristic to solve 3AP with Euclidean costs?

As is well known, assignment problems for $n$-partite graphs, with $n$>2 are NP-hard, where as assignment problems on bipartite graphs can be solved in polynomial time using the Kuhn's Hungarian ...
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### Can one find good distance-2-separators in planar graphs?

It is known that planar graphs admit "good" separators, allowing to design PTASes for specific problems such as MINIMUM INDEPENDENT SET by recursive separation of the graph. However, it seems that ...
1k views

### Sparse graphs versus dense graphs

I am curious if there are graphs problems for which either - we know that time and/or space complexity is independent of graph sparsity we do not know whether or not graph sparsity can be exploited ...
176 views

### Scaling Algorithms for the Minimum Spanning Tree Problem?

In his paper "Scaling Algorithms for Network Problems", Harold Gabow details several algorithms for graph problems that work using scaling, iteratively refining a candidate answer by beginning with a ...
444 views

### Is there a constant approximation algorithm for longest path for 3-connected cubic planar graphs or maximal planar graph?

optimization problem Input: a 3-connected cubic planar graph feasible solution: A simple path measure to optimize: length of the simple path Is there a constant approximation algorithm for this ...
538 views

### Difference between Primal Dual Algorithm for Proper and Uncrossable Functions

Williamson with many of his co-authors had worked on generalized primal dual algorithms on edge weighted graphs considering three types of functions: (1) super-modular functions (2) proper functions ...
278 views

### Good MCMC methods for exploring the space of independent sets

Let $G$ be an edge-weighted graph, and let (S, V-S) be a feasible pair if S is a maximal independent set. The weight of a feasible pair is computed by finding for each element of V-S the lightest edge ...
373 views

### Embedded dynamic programming (and planar subgraph isomorphism)

In Planar Subgraph Isomorphism Revisited, Frederic Dorn obtains an improved algorithm for Planar Subgraph Isomorphism, by using a technique he calls Embedded Dynamic Programming. This technique ...
164 views

### Finding the set of paths of smallest cumulated length that cover a given set of patterns

First of all, sorry for this long and maybe not very informative title... Context: Let $G=(V,E)$ be a directed graph, let $v_0 \in V$ be the initial node of paths that I will consider in the graph. ...
182 views

### Largest “non-disturbing” subset in a graph

The definition: The subset of vertices in a graph is called "non-disturbing" if any two vertices from this subset could be connected by a path not passing through other vertices of this subset. ...
124 views

### Grid-Minor Theorem of Robertson and Seymour and its Algorithmic Applications

Graph-Minor Theorem of Robertson and Seymour  states that if graph G has large treewidth, then it contains a large grid as minor. Most approximation results on general classes of graphs with ...
771 views

### Minimum vertex k-cut

Given an undirected graph $G = (V, E)$ and an integer $k$, the well-known minimum (edge) $k$-cut problem asks to find $E' \subseteq E$ with minimum $|E'|$ that the graph $(V, E \setminus E')$ has at ...
170 views

### Statistical Algorithms vs Convex Relaxations - Planted Clique

I am trying to understand exactly what the lower bounds for the query complexity of statistical algorithms imply for convex relaxations for the planted clique problem ? A recent paper by Feldman, ...
122 views

### General Results for Complicated Constraint Satisfaction Problem

Consider the following problem: on a finite two-dimensional grid (say the grid points are vertices of a graph), I need to color the vertices in such a way to satisfy the existence and nonexistence of ...
640 views

### Biconnected components of a directed graph?

I am looking for an algorithm for computing the biconnected components of a strongly connected directed graph.
456 views

### Weighted vertex-connectivity; global min vertex-cut

I am interested in the following problem: Input: a connected undirected graph $G=(V,E)$; a positive weight for each vertex. Output: a minimum weight subset of $V$ whose removal disconnects $G$....
985 views

### Count $k$-hop neighborhood for every vertex

For a node $v$ of a directed unweighted graph $G$, I define the $k$-hop neighborhood of $v$ as the set of vertices that are reachable from $v$ in $k$ hops or fewer (that is following a path with $k$ ...
104 views

### Evaluate polynomial involving nearly-minimal graph cuts

So you want to evaluate the polynomial $$p(x) = \sum_{C} x^{|C|}$$ where $C$ ranges over all nearly-minimum cuts in a graph (say, all minimal cuts of size $\alpha c$ where $c$ is the edge ...
240 views

### Restricted Reachability Problem

Let $G$ be a directed acyclic graph with $V$ vertices and $E$ edges. Choose some subset of $n\leq V$ "special" vertices $\{v_i\}_{i=1}^n$. How efficiently can we preprocess $(G, \{v_i\})$ so that we ...
56 views

### What are some examples of algorithmic applications of noncommutative rational identity testing?

The problem of polynomial identity testing (PIT) is known to be in $\mathsf{RP}$, but not known to be in $\mathsf{P}$. The related problem of noncommutative rational identity testing (NCIT) is known ...
256 views

### Does Depth-First-Search admit a quasilinear time algorithm in mutitape Turing Machine model?

Depth-First-Search (DFS) has a quasilinear (i.e.,$\widetilde{O}(m+n)$) time algorithm in random access model (RAM). I am curious about whether DFS still admits a $\widetilde{O}(m+n)$ time algorithm in ...
79 views

### Complexity of bounded degree full contraction

This paper defines the problem $\mathrm{B{\scriptsize OUNDED} \ D{\scriptsize EGREE}\ C{\scriptsize ONTRACTION}}$ as follows: Instance: A graph $G$ and two integers $d$ and $k$. Question: Is there a ...
Consider a partial order $P$, a series-parallel order $Q$ and a total order $R$, such that $P \subseteq Q \subseteq R$. Given $P$ and $R$, we are asked to find $Q$ of minimum length. An $O(n^3)$ ...