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Several NP-hard problems are solved exactly using exponential-time branching strategies, whether it be branch-and-bound algorithms, or bounded search trees in fixed-parameter algorithms. The number of tractable instances that can be handled…
When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…
Recently, a novel coded compressed sensing (CCS) approach was proposed in [1] for dealing with the scalability problem for large sensing matrices in massive machine-type communications. The approach is to divide the compressed sensing (CS)…
Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of…
We consider the minimum vertex cover problem having applications in e.g. biochemistry and network security. Quantum annealers can find the optimum solution of such NP-hard problems, given they can be embedded on the hardware. This is often…
In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box…
In many real-world optimization problems, more than one objective plays a role and input parameters are subject to uncertainty. In this paper, motivated by applications in disaster relief and public facility location, we model and solve a…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm…
A verification method for distributed systems based on decoupling forward and backward behaviour is proposed. This method uses an event structure based algorithm that, given a CCS process, constructs its causal compression relative to a…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems…
We consider the multiple breakpoint detection problem, which is concerned with detecting the locations of several distinct changes in a one-dimensional noisy data series. We propose the breakpointError, a function that can be used to…
Modern machine learning workloads use large models, with complex structures, that are very expensive to execute. The devices that execute complex models are becoming increasingly heterogeneous as we see a flourishing of domain-specific…
Minimizing the discrepancy of a set system is a fundamental problem in combinatorics. One of the cornerstones in this area is the celebrated six standard deviations result of Spencer (AMS 1985): In any system of n sets in a universe of size…