Related papers: A Generalization of Nemhauser and Trotter's Local …
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…
Let $\Pi$ be a hereditary graph class. The problem of deletion to $\Pi$, takes as input a graph $G$ and asks for a minimum number (or a fixed integer $k$) of vertices to be deleted from $G$ so that the resulting graph belongs to $\Pi$. This…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
Tensor optimization is crucial to massive machine learning and signal processing tasks. In this paper, we consider tensor optimization with a convex and well-conditioned objective function and reformulate it into a nonconvex optimization…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…
We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical $NP$-hard problems on graphs, such as Coloring, Vertex-Cover, and…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel determinacy technique of Marks coming from descriptive…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…
We prove that given any $\alpha$-approximation LOCAL algorithm for Minimum Dominating Set (MDS) on planar graphs, we can construct an $f(g)$-round $(3\alpha+1)$-approximation LOCAL algorithm for MDS on graphs embeddable in a given Euler…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
In this paper we give an algorithm that calculates the skeleton of a tame covering of curves over a complete discretely valued field. The algorithm relies on the {{tame simultaneous semistable reduction theorem}}, for which we give a short…
The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the…
Border complexity captures functions that can be approximated by low-complexity ones. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of…