Related papers: Reconciling Graphs and Sets of Sets
We consider variations of set reconciliation problems where two parties, Alice and Bob, each hold a set of points in a metric space, and the goal is for Bob to conclude with a set of points that is close to Alice's set of points in a…
Set reconciliation is a fundamental algorithmic problem that arises in many networking, system, and database applications. In this problem, two large sets A and B of objects (bitcoins, files, records, etc.) are stored respectively at two…
We initiate the theoretical study of directory reconciliation, a generalization of document exchange, in which Alice and Bob each have different versions of a set of documents that they wish to synchronize. This problem is designed to…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
In this work, a set reconciliation setting is considered in which two parties have similar sets that they would like to reconcile. In particular, we focus on a divide-and-conquer strategy known as partitioned set reconciliation (PSR), in…
In the standard set reconciliation problem, there are two parties $A_1$ and $A_2$, each respectively holding a set of elements $S_1$ and $S_2$. The goal is for both parties to obtain the union $S_1 \cup S_2$. In many distributed computing…
In the set reconciliation (\textsf{SetR}) problem, two parties Alice and Bob, holding sets $\mathsf{A}$ and $\mathsf{B}$, communicate to learn the symmetric difference $\mathsf{A} \Delta \mathsf{B}$. In this work, we study a related but…
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
A set $S \subseteq V$ of the graph $G = (V, E)$ is called a $[1, 2]$-set of $G$ if any vertex which is not in $S$ has at least one but no more than two neighbors in $S$. A set $S \subseteq V$ is called a $[1, 2]$-total set of $G$ if any…
Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…