相关论文: From Symmetry to Asymmetry: Generalizing TSP Appro…

The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph $G$ and a spanning tree $T$ for it, and the goal is to augment $T$ with a minimum set of edges $Aug$ from $G$, such that $T \cup Aug$…

We give a 1.25 approximation algorithm for the Steiner Tree Problem with distances one and two, improving on the best known bound for that problem.

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…

We achieve a (randomized) polynomial-time approximation scheme (PTAS) for the Steiner Forest Problem in doubling metrics. Before our work, a PTAS is given only for the Euclidean plane in [FOCS 2008: Borradaile, Klein and Mathieu]. Our PTAS…

Estimating the average degree of graph is a classic problem in sublinear graph algorithm. Eden, Ron, and Seshadhri (ICALP 2017, SIDMA 2019) gave a simple algorithm for this problem whose running time depended on the graph arboricity, but…

The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…

Approximate Simultaneous Diagonalization (ASD) is a problem to find a common similarity transformation which approximately diagonalizes a given square-matrix tuple. Many data science problems have been reduced into ASD through ingenious…

Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…

Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…

An elimination tree of a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $v$ and recursing on the connected components of $G-v$ to obtain the subtrees of $v$. The graph associahedron of $G$ is a…

Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…

Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…

In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this…

We demonstrate that adaptively controlling the size of individual regression trees in a random forest can improve predictive performance, contrary to the conventional wisdom that trees should be fully grown. A fast pruning algorithm,…

We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…

Generalised hypertree width ($ghw$) is a hypergraph parameter that is central to the tractability of many prominent problems with natural hypergraph structure. Computing $ghw$ of a hypergraph is notoriously hard. The decision version of the…

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…