arXiv subjects

Xiaoliang Li

Publications and source records attributed to Xiaoliang Li.

26 records · Page 2Linked to original sources

arXiv2021

Greenplum: A Hybrid Database for Transactional and Analytical Workloads

Demand for enterprise data warehouse solutions to support real-time Online Transaction Processing (OLTP) queries as well as long-running Online Analytical Processing (OLAP) workloads is growing. Greenplum database is traditionally known as an OLAP data warehouse system with limited ability to process OLTP workloads. In this paper, we augment Greenplum into a hybrid system to serve both OLTP and OLAP workloads. The challenge we address here is to achieve this goal while maintaining the ACID properties with minimal performance overhead. In this effort, we identify the engineering and performance bottlenecks such as the under-performing restrictive locking and the two-phase commit protocol. Next we solve the resource contention issues between transactional and analytical queries. We propose a global deadlock detector to increase the concurrency of query processing. When transactions that update data are guaranteed to reside on exactly one segment we introduce one-phase commit to speed up query processing. Our resource group model introduces the capability to separate OLAP and OLTP workloads into more suitable query processing mode. Our experimental evaluation on the TPC-B and CH-benCHmark benchmarks demonstrates the effectiveness of our approach in boosting the OLTP performance without sacrificing the OLAP performance.

cs.DB↗

arXiv2021

Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros

In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set's zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition of multivariate polynomials, and then propose an algorithm for decomposing a regular set into a finite number of simple sets. From the output of this algorithm, the multiplicities of zeros could be directly read out, and the real solution isolation with multiplicity can also be easily produced. As a main theoretical result of this paper, we analyze the structure of dual space of the saturated ideal generated by a simple set as well as a regular set. Experiments with a preliminary implementation show the efficiency of our method.

cs.SC↗

arXiv2020

Hessian quotient equations on exterior domains

It is well-known that a celebrated Jörgens-Calabi-Pogorelov theorem for Monge-Ampère equations states that any classical (viscosity) convex solution of $\det(D^2u)=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Therefore, it is an interesting topic to study the existence and uniqueness theorem of such fully nonlinear partial differential equations' Dirichlet problems on exterior domains with suitable asymptotic conditions at infinity. As a continuation of the works of Caffarelli-Li for Monge-Ampère equation and of Bao-Li-Li for $k$-Hessian equations, this paper is devoted to the solvability of the exterior Dirichlet problem of Hessian quotient equations $σ_k(λ(D^2u))/σ_l(λ(D^2u))=1$ for any $1\leq l<k\leq n$ in all dimensions $n\geq 2$. By introducing the concept of generalized symmetric subsolutions and then using the Perron's method, we establish the existence theorem for viscosity solutions, with prescribed asymptotic behavior which is close to some quadratic polynomial at infinity.

math.AP↗

arXiv2020

On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.

math.AP↗

arXiv2018

Finite time blow-up and global solutions for a nonlocal parabolic equation at high energy level

In this paper, we consider the solution of a nonlocal parabolic equation. Focusing on the solutions with initial data at high energy level, we find the criteria for global existence and finite time blow up for the corresponding solution respectively. Moreover, we prove that there always exists blow up solution with negative Nehari functional no matter how large the energy is.

math.AP↗

arXiv2017

Vacuum isolating, blow up threshold and asymptotic behavior of solutions for a nonlocal parabolic equation

In this paper, we consider a nonlocal parabolic equation associated with initial and Dirichlet boundary conditions. Firstly, we discuss the vacuum isolating behavior of solutions with the help of a family of potential wells. Then we obtain a threshold of global existence and blow up for solutions with critical initial energy. Furthermore, for those solutions satisfy $J(u_0)\leq d$ and $I(u_0)\neq 0$, we show that global solutions decay to zero exponentially as time tends to infinity and the norm of blow-up solutions increase exponentially.

math.AP↗

arXiv2013

Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.

cs.SC↗

arXiv2011

A New Algorithmic Scheme for Computing Characteristic Sets

Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for computing generalized characteristic sets by introducing other admissible reductions than pseudo-division. A concrete subalgorithm is designed to triangularize polynomial sets using selected admissible reductions and several effective elimination strategies and to replace the algorithm of basic sets (used in Ritt-Wu's algorithm). The proposed algorithm has been implemented and experimental results show that it performs better than Ritt-Wu's algorithm in terms of computing time and simplicity of output for a number of non-trivial test examples.

cs.SC↗