# Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

290 questions with no upvoted or accepted answers
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### Counting subsets of bipartite graph part which admit an induced perfect matching

Given a bipartite graph $G=(U \sqcup V, E)$, count $U^\prime \subseteq U$ for which $\exists V^\prime \subseteq V$ such that the induced subgraph $G[U^\prime \sqcup V^\prime]$ contains a perfect ...
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### Maximum weight triangles in dense graphs

There are multiple results (Vassilevska and Williams STOC09, for instance) on computing efficiently minimal-weight triangles (or more generally patterns) in node-weighted graphs. Several of these ...
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### Hardness of approximately counting independent sets with a PRAS, rather than FPRAS

It is known that approximately counting the independent sets of a graph is hard, even if randomness can be used, and even if we restrict ourselves to bounded degree graphs with degree bound at least 6....
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Can someone kindly help clarify as to exactly what is the generally accepted definition of the "sparsest cut" problem for a graph? (Isn't the set which achieves the Cheeger constant for a ...
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### Independent Sets that are Odd Covers

I am interested in a certain type of independent set I call an "odd cover". A set of vertices is independent if no two vertices in the set are connected with an edge. A set of vertices is an "odd ...
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### Is there a tight lower bound on the complexity of SSSP on a graph?

I'm an undergrad and I'm not sure if this is the right way to ask this question. I want to know the lower bound on single-source shortest path computation in a general graph. The graph is allowed to ...
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### Randomized rounding on a graph

Assume we are given an arbitrary undirected graph $G = (V, E)$ where $|V| = n$. We are also given real numbers $x_e \in [0, 1]$ for each $e \in E$. These numbers satisfy the following constraint: \...
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### Load-balancing; Alternate methods of keeping track of nodes?

Reading various articles in the literature have given me only a few decent methods of keeping track of nodes before->after load-balancing them on a very large network. One popular method uses virtual-...
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### Partitioning the vertices of a complete graph with weights on both vertices and edges with constraints

Given the complete graph on n vertices. Each vertex and each edge has a positive weight associated with it. What is desired is to partition the vertices into parts so that the sum of the weights of ...
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### K-shortest path in large sparse graph

I am an engineer and looking for a reference to find k-shortest path's in a large sparse graph. In the search for it, I came acorss Yen's ranking loopless algorithm and an improved implementation of ...
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### Finding Hamilton cycles in random graphs

For a random graph $G$ of minimum degree 3, can we find a Hamilton cycle in linear time (with high probability for every edge density)? If this is an open problem, I will also accept an empirically ...
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### Is there a poly-time algorithm to compute the drawing of a simple graph (need not be planar) in a 2D-plane such that any two edges cross at most once?

Does there exists a ploynomial time algorithm to embed a simple graph(need not be planar) in a plane satisfying the following conditions? No edge touches vertices other than its end vertices. At any ...
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### On-line pagerank in a streaming DAG (Directed Acyclic Graph)

Assume a DAG (Directed Acyclic Graph) is given as a stream of edges such that edge $(u,v)$ is given only after all incoming edges of $u$ are given. Let us denote by $n$ and $m$ the number of vertices ...
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### The Edge Cover Equilibrium Problem

Let the Edge Cover Equilibrium Problem be the following: INPUT: a simple undirected graph $G$. OUTPUT: YES, if the number of edge covers of $G$ having odd cardinality is equal to the number of edge ...
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### Variation of edge-disjoint spanning trees

In a directed graph, I want to find 2 edge-disjoint spanning trees (arborescence), with the extra restrictions that edges in the 1st tree are not forward arcs in the 2nd tree. Are there existing ...
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### Efficient game traversal of a DAG of 3-colorings

Let $X$ be a set of size $n$. Consider a game played on board $X$ by two players black and white. Starting with the empty board, each player chooses an empty spot to place a stone. Black moves ...
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### Algorithm for computing the smallest subset of nodes to remove from a graph to make it a tree

I have encountered an interesting problem that I couldn't find any references to solve: Determine the smallest subset of nodes that need to be removed from an undirected graph to make it a tree. ...
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### Common techniques for the acyclic orientation problem under some special constraint?

An acyclic orientation of an undirected graph is an assignment of a direction to each edge(an orientation) that does not form any directed cycle and therefore generates a directed acyclic graph(DAG). ...
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### Shortest s-t path when is allowed to ignore k weights

Given an undirected graph $G$ with $n$ vertices and $m$ edges, with non-negative weights on the edges, what's the best algorithm that computes the shortest path from $s$ to $t$, where you are allowed ...
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### Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
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### 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 ...