相关论文: COVID on trees and infinite grids
We propose an epidemiological model that includes the mobility patterns of the individuals, in the spirit to those considered in (Barmak, 2011, 2016) and (Medus, 2011). We assume that people move around in a city of 120x120 blocks with 300…
There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
A classical problem in Distance Geometry, with multiple practical applications (in molecular structure determination, sensor network localization etc.) is to find the possible placements of the vertices of a graph with given edge lengths.…
COVID-19 outbreaks have proven to be very difficult to isolate and extinguish before they spread out. An important reason behind this might be that epidemiological barriers consisting in stopping symptomatic people are likely to fail…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…
Vertex deletion to hereditary graph class is well-studied in parameterized complexity. Vertex deletion to the scattered graph classes has gained attention in recent years. In this paper, we consider (Proper-Interval, Tree)-Vertex Deletion,…
We study the Short Path Packing problem which asks, given a graph $G$, integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$ pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The problem has…
We analyze a game-theoretic abstraction of epidemic containment played on an undirected graph $G$: each player is associated with a node in $G$ and can either acquire protection from a contagious process or risk infection. After decisions…
In this paper, we consider the following \emph{$k$-many firefighter problem} on a finite graph $G=(V,E)$. Suppose that a fire breaks out at a given vertex $v \in V$. In each subsequent time unit, a firefighter protects $k$ vertices which…
Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…
Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts -- offline and online social networks,…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
Let $G=(V,E)$ and $H$ be two graphs. Packing problem is to find in $G$ the largest number of independent subgraphs each of which is isomorphic to $H$. Let $U\subset{V}$. If the graph $G-U$ has no subgraph isomorphic to $H$, $U$ is a cover…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al.~a decade ago, and only by then we…
The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…