相关论文: Computing $\vec{\mathcal{S}}$-DAGs and Parity Game…

We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…

Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small…

In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

Thomas proved that every undirected graph admits a linked tree decomposition of width equal to its treewidth. In this paper, we generalize Thomas's theorem to digraphs. We prove that every digraph G admits a linked directed path…

We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…

Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…

Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow,…

Given a simple graph $G$, a weight function $w:E(G)\rightarrow \mathbb{N} \setminus \{0\}$, and an orientation $D$ of $G$, we define $\mu^-(D) = \max_{v \in V(G)} w_D^-(v)$, where $w^-_D(v) = \sum_{u\in N_D^{-}(v)}w(uv)$. We say that $D$ is…

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…

We study analogues of $\mathcal{F}$-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. We examine analogous games on directed graphs, and show tight results on the walk-avoiding game. We also…

Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix…

It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show…

We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…

Tree-cut width is a graph parameter introduced by Wollan that is an analogue of treewidth for the immersion order on graphs in the following sense: the tree-cut width of a graph is functionally equivalent to the largest size of a wall that…

This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…

We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized coloring numbers. Our parameters are based on new…

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous…