Related papers: Relaxed Survey Propagation for The Weighted Maximu…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

We analyse the asymptotic behaviour of random instances of the Maximum Set Packing (MSP) optimization problem, also known as Maximum Matching or Maximum Strong Independent Set on Hypergraphs. We give an analytical prediction of the MSPs…

We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli…

This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of…

We consider regularized least-squares problems of the form $\min_{x} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \mathcal{R}(Lx)$. Recently, Zheng et al., 2019, proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a…

The Max-k-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic NP-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-k-Cut, they often lack guarantees of…

In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…

We consider an extension of the set covering problem (SCP) introducing (i)~multicover and (ii)~generalized upper bound (GUB)~constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and…

The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…

We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate a MAX-SAT solver, it is convenient to generate hard MAX-SAT instances with…

The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…

Optimal sensor placement (SP) usually minimizes an impact measure, such as the amount of contaminated water or the number of inhabitants affected before detection. The common choice is to minimize the minimum detection time (MDT) averaged…

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…

We extend to the random K-SAT and p-XOR-SAT optimization problems the results obtained for the Viana-Bray model of diluted mean field spin glass.

In this letter, we show how the Survey Propagation algorithm can be generalized to include external forcing messages, and used to address selectively an exponential number of glassy ground states. These capabilities can be used to explore…

Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most…

This paper addresses the Kidnapped Robot Problem (KRP), a core localization challenge of relocalizing a robot in a known map without prior pose estimate upon localization loss or at SLAM initialization. For this purpose, a passive 2-D…

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…