Related papers: Graph Search Trees and Their Leaves
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
Broadcasting in a computer network is a method of transferring a message to all recipients simultaneously. It is common in this situation to use a tree with many leaves to perform the broadcast, as internal nodes have to forward the…
Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixed-depth minimax tree-search algorithm traversing a uniform tree must explore, the so-called minimal tree. Since real-life minimax trees are not…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense,…
With XML becoming an ubiquitous language for data interoperability purposes in various domains, efficiently querying XML data is a critical issue. This has lead to the design of algebraic frameworks based on tree-shaped patterns akin to the…
The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single source node to all the nodes reachable…
Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support…
Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…
It is known that the online firefighting is 2-competitive on trees (Coupechoux et al. 2019), which suggests that the problem is relatively easy on trees. We extend the study to graphs containing cycles. We first show that the presence of…
A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…
The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for the efficient implementation of DFS-based graph algorithms and exemplify them on three algorithms for computing strongly…
Let $T$ be a tree, a vertex of degree one and a vertex of degree at least three is called a leaf and a branch vertex, respectively. The set of leaves of $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$…
We prove, that every connected graph with $s$ vertices of degree 3 and $t$ vertices of degree at least~4 has a spanning tree with at least ${2\over 5}t +{1\over 5}s+\alpha$ leaves, where $\alpha \ge {8\over 5}$. Moreover, $\alpha \ge 2$ for…