Related papers: Practical optimization of Steiner Trees via the ca…
We study the Sum of Squares (SoS) Hierarchy with a view towards combinatorial optimization. We survey the use of the SoS hierarchy to obtain approximation algorithms on graphs using their spectral properties. We present a simplified proof…
Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees.…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…
The weighted sum method is a simple and widely used technique that scalarizes multiple conflicting objectives into a single objective function. It suffers from the problem of determining the appropriate weights corresponding to the…
A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is…
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…
A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to…
We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…
We give a simple approximation algorithm for a common generalization of many previously studied extensions of the maximum size stable matching problem with ties. These generalizations include the existence of critical vertices in the graph,…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice.…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a…
Bounded Max-Sum (BMS) is a message-passing algorithm that provides approximation solution to a specific form of de-centralized coordination problems, namely Distributed Constrained Optimization Problems (DCOPs). In particular, BMS algorithm…
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…
Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most…