Algorithms on graphs, excluding heuristics.
-1
votes
0answers
19 views
Find a max flow in a flow network that passes through a fixed number of nodes
I want to solve a network flow problem with the usual setup of a directed graph with a capacity value for each edge. However, I also have an additional constraint: I want to find the maximum flow ...
2
votes
0answers
22 views
2-hop Labelings for \#Shortest-Paths Queries
Given a graph $G = (V, E)$, it is possible to find a shortest distance labeling $(L, F)$ for $G$ such that for each $u, v \in V$, we have
$$
d(u, v) = F(L(u), L(v))
$$
where $d(u, v)$ is the shortest ...
2
votes
0answers
57 views
randomly sample a degeneracy ordering
Given an undirected graph $G$, the $k$-core of $G$ is defined as the maximal subgraph such that each vertex has at least $k$ neighbors in the subgraph. The cores of $G$ can be computed by the ...
1
vote
1answer
41 views
Problem property name where an optimal solution in a graph can be used as a solution in any subgraph
Suppose one is given a graph optimization problem where the optimal solution $S$ for the problem on graph $G$ can be used as a solution for any subgraph of $G$. In other words, given $S$ is an optimal ...
-2
votes
0answers
24 views
Calling this Reeds-Shepp implementations
I am pretty new to coding and am working on a path planner that requires minimum reeds shepp curve length as input. For this I found an old piece of code written by S. Lavalle which can be found here:
...
5
votes
1answer
96 views
Counting/Enumerating Minimal Edge Covers
A Minimal Edge Cover is an Edge Cover such that no other Edge Cover is a proper subset of it.
Questions
Which is the complexity of counting Minimal Edge Covers? Do we know any non-trivial ...
-1
votes
0answers
37 views
How to randomly sample a social graph to find paths between at least 20% of profiles?
Given a Graph, where we know
Total number of nodes (~100,000)
Average no of connections per node (~200)
Maximum distance between two nodes (~5)
How many nodes (and its connections) do we have to ...
0
votes
0answers
38 views
Efficient topological sorting of the cartesian product of DAGs
Let us consider n directed acyclic graphs $(G_i)_{1\leq i \leq n}$ and G their cartesian product (with the induced edges) : G is still a DAG.
Let us suppose that each vertex has a value, defined as ...
1
vote
1answer
66 views
Color shifting in a bipartite graph
Assume that we have a directed bipartite graph $G = \langle L\dot\cup R, E\rangle $. Where $E$ contains directed edges only from $L$ to $R$, that is, $E\subseteq L\times R$. Assume further that the ...
2
votes
0answers
75 views
Counting the maximum number of paths of length $n$ that differ in at least $k$ edges
What is known about the complexity of solving (or approximately solving) the following problem?
INPUT: Graph $G=(V,E)$ and constants $L$ and $K$.
OUTPUT: The maximum size of any set $S$ of simple ...
1
vote
0answers
48 views
Reduction of irregular graphs, to regular graphs, while preserving hamiltonicity
I am wondering if this is a topic that has had research done...
If I could reduce irregular graphs to regular graphs (including replacing redundant node clusters with dummy nodes), while ensuring ...
0
votes
0answers
66 views
Partitioning directed graph
I'm a newbie in the mathematical field of graph theory (started to dive into it only few days ago) but I'm a very fast learner and have deep mathematical background. I'm trying to find/develop an ...
8
votes
1answer
181 views
Could chromatic number be easy to calculate when colouring is hard for some graph class?
Similar question was asked before, but there was an error in it so it was left unanswered Graph class with easy chromatic number, but NP-hard coloring
Is there any infinite set of graphs $C$ such as:
...
0
votes
0answers
33 views
Minimum cost circulation problem with bounded number of edges
Note: the question was taken from https://cs.stackexchange.com/questions/95479/minimum-cost-circulation-problem-with-bounded-number-of-edges
Since there was no answer in that forum (even after ...
2
votes
0answers
144 views
A variant of the Maximum Weight Clique problem
I am trying to solve a problem that I could reduce to the following:
Given a graph $G=(V,E)$ with both edge and vertex weights, all weights being non-negative, find a clique $Q\subseteq V$ s.t. $\sum_{...
3
votes
2answers
146 views
Finding a set which dominates the Minimum Dominating Set
Given an unweighted, undirected graph, a dominating set $S$ is a set of nodes such that every node is in $S$ or adjacent to a node in $S$.
The dominating set problem is NP-hard, but I am considering ...
4
votes
2answers
124 views
Max cut problem between two connected subgraphs
Let $G$ be a connected graph.
Consider the problem of finding a partition $G = A \cup B$ into connected subgraphs, so that the cut between $A$ and $B$ is maximized. Is there anything which is known ...
-2
votes
1answer
97 views
Finding Cheapest n-Path [closed]
Given a weighted directed acyclic graph, how can I find the cheapest path from an Origin Vertex to a Destination Vertex which ...
2
votes
0answers
37 views
Min cut problem on unbalanced partitions for planar graphs with unit capacity edges
The question is: given a planar graph $G$ with unit capacity edge weights and a fixed positive integer $k$, what is an approximation algorithm for finding the minimum size of a cut $(A,B)$ with $|A|=k$...
4
votes
1answer
80 views
Exact algorithm or parameterized algorithm for Maximum Edge Biclique Problem?
The Maximum Edge Biclique(MEB) problem is to find a biclique with as many edges as possible in a bipartite graph. It was proved to be NP-complete by Peeters in 2003, and then the inapproximability ...
4
votes
1answer
114 views
Fast algorithm to find a maximum connected subgraph of k vertices
Given an undirected graph $G = (V, E)$ and a function $f: 2^V \to \mathbb{R}^+,$ where $2^V$ is the set of all subsets of $V$. Find a connected subgraph $T = (V_T, E_T)$ of k vertices such that $f(V_T)...
3
votes
1answer
107 views
Finding a “lowest” path in a graph
I have an undirected graph $G = (E,V)$, $|V|=n$,
where each node $v_i$ has a natural number weight.
Think of these weights as heights $h_i$.
Given two nodes $s$ and $t$, I'd like to find a lowest ...
4
votes
2answers
138 views
Check if graph stays connected after edge swap
Checking whether a (simple, undirected) graph is connected can be done in linear time in the number of edges. What I am looking for is a more efficient way of checking whether it stays connected after ...
3
votes
1answer
154 views
What exactly is Lawler's modification to Yen's algorithm and how does it work?
I recently read about Yen's algorithm, I understand the algorithm and it seems correct, however Wikipedia mentions that there exists "Lawler's modification" to the algorithm, which is described as ...
4
votes
1answer
296 views
Minimum Union-Sum Cost Path
I have a minimum cost path selection problem that is different from the usual shortest path in that each type of cost is accounted only once in the total cost of the path if multiple edges on the path ...
1
vote
0answers
49 views
k-center 2.0: A stronger k-center condition
Given an unweighted, undirected graph, we can use the classical 2-appx for $k$-center to select a set $S$ of centers such that every vertex is within a distance of 2 of some center in $S$.
Note that ...
3
votes
1answer
47 views
Complexity of distributively verifying that the diameter is small
Consider a graph $G=(V,E)$ and an integer parameter $k$.
I'm interested in the round complexity, in the CONGEST model, of checking if the diameter of the graph is "much larger" or "much smaller" than ...
0
votes
0answers
21 views
is there any result on mTSP over highly structured/modular graphs?
I am looking for theoretical results on mTSP (multiple travelling salesmen problem) over structured/modular graphs. If the meaning of "modular" is not clear, think about a graph that represents a ...
0
votes
0answers
24 views
explicit UES for $D$-regular graphs over $N$ vertices through the line graph
First of all observe that if we have $G$, a $D$-regular graph over $N$ vertices that is equipped with a consistent labeling $\ell$ then we can induce a consistent labeling for $L(G)$ the line graph of ...
0
votes
0answers
55 views
How to find cyclic ordering of edges incident on a vertex in a plane graph?
(I asked this on mathse. May be it suits better here)
How to find the cyclic ordering of edges incident on a vertex in a plane graph? (ie, in a plane embedding) Of coure we are looking for a ...
6
votes
1answer
193 views
Computing topological sort while keeping edges “short”
Motivation: I want to compute a topological sort order in which the connected vertices are close to each other.
Problem statement: Given a DAG $G(V,E)$ with $n$ vertices, compute a topological sort ...
0
votes
1answer
51 views
What is the deterministic complexity of counting the number of global minimum cuts on an unweighted undirected graph?
I know as a consequence of Karger's algorithm that the number of minimum cuts is bounded by $\binom{n}{2}$. In the comments of
Counting the number of distinct s-t cuts in a oriented graph
It says ...
6
votes
1answer
131 views
Partition edges into edge disjoint walks
Consider an undirected graph $G=(V,E)$ and two sequences of $k$ vertices $S=s_1,\ldots,s_k$ and $T=t_1,\ldots,t_k$.
A set of $k$ walks is called a $(S,T)$-walk partition if
the walks form a ...
3
votes
0answers
108 views
Is 3-coloring bounded degree graphs subexponential: $O(\exp{(\sqrt{n}\log^2{n})})$? [closed]
We got an argument that 3-coloring bounded degree graphs is subexponential
with complexity $O(\exp{(\sqrt{n}\log^2{n})})$.
The treewidth of a planar graphs on $n$ vertices is $O(\sqrt{n})$
and 3-...
5
votes
1answer
150 views
“Smallest” path that visits a given set of vertices
I use smallest rather than shortest to distinguish between the shortest path problem. The problem is as follows:
Given a directed graph $G=(V,E)$, two vertices $s$ and $t$, and a set of $p$ ...
1
vote
1answer
86 views
What is the best and easy (regarding implementation) way of computing three edge independent trees in a 3-connected graph?
I am searching for an implementation of an algorithm that constructs three edge independent spanning trees from a 3-edge connected graph. Any response will be appreciated. Thanks in Advance.
8
votes
2answers
310 views
Counterexample to max-flow algorithms with irrational weights?
It is known that Ford-Fulkerson or Edmonds-Karp with the fat pipe heuristic (two algorithms for max-flow) need not halt if some of the weights are irrational. In fact, they can even converge on the ...
13
votes
1answer
324 views
What are the obstructions to extending $L=SL$ to $L=NL$?
Omer Reingold's proof that $L=SL$ gives an algorithm for USTCON (In an Undirected graph with special vertices $s$ and $t$, are they Connected?) using only logspace. The basic idea is to build an ...
0
votes
0answers
60 views
Hypergraph Coloring Complexity
Dear can you help I am confused about the complexity of hypergraph coloring and finding the minimum number of colors
Finding the minimum number of colors for strongly coloring a k-uniform hypergraph ...
1
vote
2answers
173 views
Is perfect matching for bipartite graph with no cycles unique?
Given a balanced bipartite graph that satisfies Hall's theorem (is non singular) then it shown that it has at least one perfect matching.
My question is if the balanced bipartite graph is also ...
-1
votes
1answer
160 views
Closeness Centrality for Weighted Graphs
In order to determine the Closeness Centrality for a vertex u in a graph, you compute the shortest path between u and all other vertices in the graph. The centrality is then given by:
$C(u) = \frac{1}...
0
votes
0answers
64 views
Path Finding: single-source, multi-path, multi-target, and max-depth - approaches and application
Background
Definitions (as used here):
$\qquad$single-source: for path finding, an algorithm is single-source if it searches from a given node.
$\qquad$multi-target: for path finding, an ...
6
votes
0answers
72 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 ...
0
votes
0answers
53 views
Find the maximum induced (weighted) subgraph with edge weights greater than some minimum
I have a (fully connected) weighted undirected graph.
I want to find a maximal induced subgraph whose edge weights are all above some minimum value.
Or, if not a maximal subgraph, then with some ...
5
votes
0answers
163 views
Find a pair of nodes with maximum sum of distances in k given trees
For k edge-weighted trees $T_1,T_2...T_k$ which contain the same set of nodes $\{1,2,... n \}$, I want to find a pair of nodes $(x,y)$ which maxifies $$\sum_{i=1}^k d_i(x,y)$$ where $d_i(x,y)$ ...
3
votes
0answers
97 views
Graph-related applications of the fast Fourier transform (and other algebraic algorithms)
The fast matrix multiplication algorithm is useful for numerous graph problems (e.g. matchings and shortest paths).
However, while the fast Fourier transform algorithm implies several other near-...
15
votes
1answer
390 views
What is the complexity of this graph problem?
Given a simple undirected graph $G$, find a subset $A\neq \emptyset$ of vertices, such that
for any vertex $x\in A$ at least half of the neighbors of $x$ are also in $A$, and
the size of $A$ is ...
2
votes
1answer
109 views
What is the name of this algorithm on direct acyclic graph?
I am trying to linearize the history of a git branch for display purpose. I want commits to be collocated by branch instead of simply displaying commits in the order given by the time of commit.
In ...
0
votes
0answers
28 views
Partitions of regular graphs with upper bounds on bipartition width
Are there efficient graph partitioning algorithms with guaranteed upper bounds on the bipartition width in terms of the total number of vertices of the graph, or another non-spectral quantity (...
1
vote
0answers
90 views
Generalized path cover problem in DAG
Let $G=(V,E)$ be a directed acyclic graph. Two vertices is transitive if there is a directed path between them. A Path Cover for a Set of Transitive Pairs (PCSTP) is a set of directed paths such that ...
