Related papers: Stabilizer Approximation III: Maximum Cut
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
The number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though various approaches have been proposed to compute it, the gap…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Trevisan [SICOMP 2012] presented an algorithm for Max-Cut based on spectral partitioning techniques. This is the first algorithm for Max-Cut with an approximation guarantee strictly larger than 1/2 that is not based on semidefinite…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in time $n^{O(k)}$, where $k$ is the treewidth of the graph. This improves on the previous $2^{2^k}$-approximation in time $\poly(n) 2^{O(k)}$ due to Chlamt\'a\v{c}…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…
We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
We prove that, for every integer $d$ with $d\geq 3$, there is an approximation algorithm for the maximum induced matching problem restricted to $\{ C_3,C_5\}$-free $d$-regular graphs with performance ratio $0.708\bar{3}d+0.425$, which…
In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on…
Getting a labeling of vertices close to the structure of the graph has been proved to be of interest in many applications e.g., to follow smooth signals indexed by the vertices of the network. This question can be related to a graph…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…
We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…