Related papers: On the Maximum Distance Sublattice Problem and Clo…
The maximum covering location problem (MCLP) is a key problem in facility location, with many applications and variants. One such variant is the dynamic (or multi-period) MCLP, which considers the installation of facilities across multiple…
In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset,…
We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several…
In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find…
The geometric $\delta$-minimum spanning tree problem ($\delta$-MST) is the problem of finding a minimum spanning tree for a set of points in a normed vector space, such that no vertex in the tree has a degree which exceeds $\delta$, and the…
The Molecular Distance Geometry Problem (MDGP) is essential in structural biology, as it seeks to determine three-dimensional protein structures from partial interatomic distances. Its discretizable subclass (DMDGP) admits an exact…
Given a weighted undirected graph $G=(V,E,d)$, the Molecular Distance Geometry Problem (MDGP) is that of finding a function $x:G\to \mathbb{R}^{3}$, where $||x(u)-x(v)||=d(u,v)$ for each $\{u,v\}\in E$. We show that under a few assumptions…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
We introduce a new class of algorithms for finding a short vector in lattices defined by codes of co-dimension $k$ over $\mathbb{Z}_P^d$, where $P$ is prime. The co-dimension $1$ case is solved by exploiting the packing properties of the…
In this work, we give provable sieving algorithms for the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) on lattices in $\ell_p$ norm ($1\leq p\leq\infty$). The running time we obtain is better than existing provable…
The Minimum Eccentricity Shortest Path (MESP) Problem consists in determining a shortest path (a path whose length is the distance between its extremities) of minimum eccentricity in a graph. It was introduced by Dragan and Leitert [9] who…
We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the…
The discrete Gaussian $D_{L- t, s}$ is the distribution that assigns to each vector $x$ in a shifted lattice $L - t$ probability proportional to $e^{-\pi \|x\|^2/s^2}$. It has long been an important tool in the study of lattices. More…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
Evolution of large scale networks demand for efficient way of communication in the networks. One way to propagate information in the network is to find vertex cover. In this paper we describe a variant of vertex cover problem naming it…
This paper studies the lattice agreement problem and proposes a stronger form, $\varepsilon$-bounded lattice agreement, that enforces an additional tightness constraint on the outputs. To formalize the concept, we define a quasi-metric on…
The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…
Given a parametric lattice with a basis given by polynomials in Z[t], we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: that is, they are given by formulas that are piecewise…
In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum…
The shortest vector problem (SVP) over ideal lattices is closely related to the Ring-LWE problem, which is widely used to build post-quantum cryptosystems. Power-of-two cyclotomic fields are frequently adopted to instantiate Ring-LWE. Pan…