Related papers: Approximation Hardness of Graphic TSP on Cubic Gra…
Recently, there has been interest in the question of whether a partial matrix in which many of the fully defined principal submatrices are PSD is approximately PSD completable. These questions are related to graph theory because we can…
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…
In the context of stationary $\mathbb{Z}^d$ nearest-neighbour Gibbs measures $\mu$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property (TSSM)) on the support of $\mu$…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
In the Strip Packing problem (SP), we are given a vertical half-strip $[0,W]\times[0,\infty)$ and a set of $n$ axis-aligned rectangles of width at most $W$. The goal is to find a non-overlapping packing of all rectangles into the strip such…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
In this paper, we give a simple polynomial-time reduction of {L(p)-Labeling} on graphs with a small diameter to {Metric (Path) TSP}, which enables us to use numerous results on {(Metric) TSP}. On the practical side, we can utilize various…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
A $k$-dimensional box is the Cartesian product $R_1 \times R_2 \times ... \times R_k$ where each $R_i$ is a closed interval on the real line. The {\it boxicity} of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$…
The \textit{toughness} $t(G)$ of a graph $G$ is a measure of its connectivity that is closely related to Hamiltonicity. Brouwer proved the lower bound $t(G) > \ell / \lambda - 2$ on the toughness of any connected $\ell$-regular graph, where…
We construct 2-query, quasi-linear size probabilistically checkable proofs (PCPs) with arbitrarily small constant soundness, improving upon Dinur's 2-query quasi-linear size PCPs with soundness $1-\Omega(1)$. As an immediate corollary, we…
This paper proves strong lower bounds for distributed computing in the CONGEST model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts. The contribution of bit-gadgets is twofold. First, developing…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding $f:K\to R^2$. Analogous notions were studied in computer science under the names of…
\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database.…
Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness…
The 2-distance coloring of a graph $G$ is equivalent to the proper coloring of its square graph $G^2$, it is a special distance labeling problem. DP-coloring (or "Correspondence coloring") was introduced by Dvo\v{r}\'ak and Postle in 2018,…
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the $(1,2)$-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on…