Related papers: Cut Tree Construction from Massive Graphs
Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are classical well-investigated objects. Their (parameterized) complexity and efficiently tractable cases have been studied. In the present paper, for a given set of…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…
Tree-width and path-width are widely successful concepts. Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width. Many efficient algorithms are based on a tree decomposition. Sometimes the more…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known…
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on…
Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is $k$-connected if it remains connected after removing any $k-1$ vertices. The vertex connectivity of a graph is the maximum $k$ such that…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
Gradient Boosted Decision Trees (GBDTs) are dominant machine learning algorithms for modeling discrete or tabular data. Unlike neural networks with millions of trainable parameters, GBDTs optimize loss function in an additive manner and…