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We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias,…
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but…
Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes coincides with an important dichotomy in universal algebra; in…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…
Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…