相关论文: Edge-Disjoint Spanning Trees on Star-Product Netwo…

Delivery systems have become a core part of urban life, supporting the demand for food, medicine, and other goods. Yet traditional logistics networks remain fragile, often struggling to adapt to road closures, accidents, and shifting…

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…

Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…

The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph $G$ with ${n+1\choose 2}$ edges admits an edge decomposition $G=H_1\oplus\cdots \oplus H_n$ such that $H_i$ has $i$ edges and it is isomorphic to a subgraph of…

For a digraph $D=(V(D),A(D))$ and a set $S\subseteq V(D)$ with $|S|\geq 2$ and $r\in S$, a directed pendant $(S,r)$-Steiner tree (or, simply, a pendant $(S,r)$-tree) is an out-tree $T$ rooted at $r$ such that $S\subseteq V(T)$ and each…

Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…

Edge bundling techniques cluster edges with similar attributes (i.e. similarity in direction and proximity) together to reduce the visual clutter. All edge bundling techniques to date implicitly or explicitly cluster groups of individual…

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…

This work presents a topology detection method combining home smart meter information and sparse line flow measurements. The problem is formulated as a spanning tree detection problem over a graph given partial nodal and edge flow…

The celebrated Nash-Williams and Tutte's theorem states that a graph $G=(V, E)$ contains $k$ edge disjoint spanning trees if and only if $\nu_{f}(G) \geq k$, where $$\nu_{f}(G):=\min_{|\mathcal{\mathcal{P}}|>1, \text{$\mathcal{P}$ is a…

Recent studies shows that the majority of existing deep steganalysis models have a large amount of redundancy, which leads to a huge waste of storage and computing resources. The existing model compression method cannot flexibly compress…

Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…

Since 1997 there has been a steady stream of advances for the maximum disjoint paths problem. Achieving tractable results has usually required focusing on relaxations such as: (i) to allow some bounded edge congestion in solutions, (ii) to…

Along with the development of manufacture and services, the problem of distribution network optimization has been growing in importance, thus receiving much attention from the research community. One of the most recently introduced network…

Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…

Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…

We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of…

Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…

Let $G=(V,E)$ be a multigraph with a set $T\subseteq V$ of terminals. A path in $G$ is called a $T$-path if its ends are distinct vertices in $T$ and no internal vertices belong to $T$. In 1978, Mader showed a characterization of the…

In phylogenetics, reconstructing rooted trees from distances between taxa is a common task. B\"ocker and Dress generalized this concept by introducing symbolic dated maps $\delta:X \times X \to \Upsilon$, where distances are replaced by…