Related papers: Explicit Polyhedral Bounds on Network Coding Rate …
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We consider the verification of parameterized networks of replicated processes whose architecture is described by hyperedge-replacement graph grammars. Due to the undecidability of verification problems such as reachability or coverability…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social,…