Related papers: Parallel Approximation and Integer Programming Ref…
Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…
We show that global constraints on finite domains like all-different can be reformulated into answer set programs on which we achieve arc, bound or range consistency. These reformulations offer a number of other advantages beyond providing…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
The Resource Constrained Shortest Path Problem (RCSPP) is a fundamental combinatorial optimisation problem in which the goal is to find a least-cost path in a directed graph subject to one or more resource constraints. In this paper we…
We consider approximation algorithms for packing integer programs (PIPs) of the form $\max\{\langle c, x\rangle : Ax \le b, x \in \{0,1\}^n\}$ where $c$, $A$, and $b$ are nonnegative. We let $W = \min_{i,j} b_i / A_{i,j}$ denote the width…
It is now well known that sparse or compressible vectors can be stably recovered from their low-dimensional projection, provided the projection matrix satisfies a Restricted Isometry Property (RIP). We establish new implications of the RIP…
In 1982, Lagarias showed that solving the approximate Shortest Vector Problem also solves the problem of finding good simultaneous Diophantine approximations. Here we provide a deterministic, dimension-preserving reduction in the reverse…
We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
$ \newcommand{\SVP}{\textsf{SVP}} \newcommand{\CVP}{\textsf{CVP}} \newcommand{\eps}{\varepsilon} $We show a number of reductions between the Shortest Vector Problem and the Closest Vector Problem over lattices in different $\ell_p$ norms…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…