Related papers: Interacting Copies of Random Constraint Satisfacti…
We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which type of clusters of solutions are addressed by different…
In the quantum optimisation setting, we build on a scheme introduced by Young et al [PRA 88, 062314, 2013], where physical qubits in multiple copies of a problem encoded into an Ising spin Hamiltonian are linked together to increase the…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of $k$-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…
Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a "threshold saturation"…
We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such…
Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;…
We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
A statistical-mechanical study of the effect of constraint relaxation on the minimum vertex cover problem in Erd\H{o}s-R\'enyi random graphs is presented. Using a penalty-method formulation for constraint relaxation, typical properties of…
Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…