# Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

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### Latest results on the k-stacker crane problem?

I was searching for the $k$-stacker crane problem on google scholar but the best known result is dated back to 1976 with the original paper. I'm unsure whether there would be newer results of the ...
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### Bipartite graph projections, with threshold

Let $G=(\top,\bot,E)$ be a bipartite graph: $E\subseteq \top\times\bot$. The projections $G_\bot = (\bot,E_\bot)$ and $G_\top = (\top,E_\top)$ of $G$ are defined as follows: two vertices are linked ...
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### Maximum weight matching with classes of edges in a multi-edge bipartite graph

Posted a similar question in mathoverflow, have tried to reduce this to Ford Fulkerson, but been stuck. Thought I'd ask TCS community to see if there are any ideas from individuals, here. Consider a ...
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### Is this node permutation optimization NP-Hard?

Let $G=(V,E)$ be an undirected graph and let $\pi$ be a permutation of the vertices in $V$. For a node $v\in V$, we denote by $\text{succ}_{\pi}(v)$ the set of neighbors of $v$ that occur after $v$ in ...
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### Dynamic connectivity with known history, for maximal connected component span

Consider a graph in which edges are added and removed over time. Define the span of a connected component as the product of its number of vertices and the longest duration for which it remains a ...
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### Is this problem in P? Given a bipartite graph, find a minimum cardinality set of edges which intersect every vertex cover

This problem came up in my study of digraphs: Given a connected bipartite graph $G = (A \cup B, E)$, a vertex cover is a set $S$ of vertices such that every edge has some endpoint in $S$. Note that $A$...
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### Graphs-like data structure with weighted vertices

I am searching for literature related to a graph-like data structure where vertices are weighted instead of edges. Formally, we can define a weighted-(edge)-graph $G=(V,E, w(\cdot))$ as a tuple of ...
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### Complexity of acyclicity of a “nondeterministic” graph

By "nondeterministic" I mean the graph is a collection of sets of "candidate" edges sharing a single destination: $E \subseteq 2^V \times V$. The problem is whether it is possible ...
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### granularity of bidirectional breadth-first search

I tried posting this on stack overflow and it got no takers, decided to cross post here: One thing that I've never seen discussed about bidirectional breadth-first-search (which I'll abbreviate as ...
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### Sample graph dataset for testing algorithms

I hope I'm addressing the right community. For a project for my students, I need to find some weighted graphs (oriented or not) to benchmark their algorithms (shortest paths, flows...). There are a ...
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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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### Find min-weight simple path assuming no negative simple cycles

A simple path is a path that doesn't revisit a node. A simple cycle is a cycle that doesn't revisit an edge. You are given an undirected graph G which may contain edges of negative weight but which ...
Let's assume that we are given two graphs $G_1$ and $G_2$ defined by the two following nicely drawn pictures. Black numbers label the nodes, red numbers show the edge weight between the nodes. $G_1$ ...