Related papers: Multi-Party Set Reconciliation Using Characteristi…
As users migrate information to cloud storage, many distributed cloud-based services use multiple loosely consistent replicas of user information to avoid the high overhead of more tightly coupled synchronization. Periodically, the…
We consider a set reconciliation setting in which two parties hold similar sets which they would like to reconcile In particular, we focus on set reconciliation based on invertible Bloom lookup tables (IBLTs), a probabilistic data structure…
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…
We consider the problem of reconstructing the symmetric difference between similar sets from their representations (sketches) of size linear in the number of differences. Exact solutions to this problem are based on error-correcting coding…
We explore a generalization of set reconciliation, where the goal is to reconcile sets of sets. Alice and Bob each have a parent set consisting of $s$ child sets, each containing at most $h$ elements from a universe of size $u$. They want…
Set reconciliation, where two parties hold fixed-length bit strings and run a protocol to learn the strings they are missing from each other, is a fundamental task in many distributed systems. We present Rateless Invertible Bloom Lookup…
Multipartite entity resolution aims at integrating records from multiple datasets into one entity. We derive a mathematical formulation for a general class of record linkage problems in multipartite entity resolution across many datasets as…
Set reconciliation protocols typically make two critical assumptions: they are designed for fixed-sized elements and they are optimized for when the difference cardinality, d, is very small. When adapting to variable-sized elements, the…
In this paper, we initiate a study of a new problem termed function computation on the reconciled data, which generalizes a set reconciliation problem in the literature. Assume a distributed data storage system with two users $A$ and $B$.…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
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…
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…
Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…
The Distributed Bloom Filter is a space-efficient, probabilistic data structure designed to perform more efficient set reconciliations in distributed systems. It guarantees eventual consistency of states between nodes in a system, while…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $\rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…