Related papers: From one solution of a 3-satisfiability formula to…
We present a topological barrier to efficient computation, revealed by comparing the geometry of 2 SAT and 3 SAT solution spaces. Viewing the set of satisfying assignments as a cubical complex within the Boolean hypercube, we prove that…
It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product…
For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust…
One of the most intriguing dynamics in biological systems is the emergence of clustering, the self-organization into separated agglomerations of individuals. Several theories have been developed to explain clustering in, for instance,…
An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…
We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to…
There has been much recent interest in the satisfiability of random Boolean formulas. A random k-SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known…
In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of high density that we call cluster cores. We then consider a random walk on a…
We extend the single-site coherent potential approximation (CPA) to include the effects of non-local disorder correlations (alloy short-range order) on the electronic structure of random alloy systems. This is achieved by mapping the…
Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3-SAT is equivalent to…
Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We introduce a simple, intuitive and yet powerful algorithm for clustering analysis. This algorithm is an iterative process on the sample space, which arises as an extension of the iteratively generated correlation matrices. It allows for…
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned…
Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…
This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three $\mathrm{3SAT}$: $\mathrm{P} = \mathrm{NP}$." Salum purports to give a polynomial-time algorithm that solves the $\mathrm{NP}$-complete…
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of…