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We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$…
A graph $G$ is embeddable in $\mathbb{R}^d$ if vertices of $G$ can be assigned with points of $\mathbb{R}^d$ in such a way that all pairs of adjacent vertices are at the distance 1. We show that verifying embeddability of a given graph in…
Bayes nets are extensively used in practice to efficiently represent joint probability distributions over a set of random variables and capture dependency relations. In a seminal paper, Chickering et al. (JMLR 2004) showed that given a…
We give a new, elementary proof of what we believe is the simplest known example of a ``natural'' problem in computational 3-dimensional topology that is $\mathsf{NP}$-hard -- namely, the \emph{Trivial Sublink Problem}: given a diagram $L$…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if…
While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…
We show that finding a graph realization with the minimum Randi\'c index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found…
The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $\sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=\cup_{i=1}^s…
Node-connectivity augmentation is a fundamental network design problem. We are given a $k$-node connected graph $G$ together with an additional set of links, and the goal is to add a cheap subset of links to $G$ to make it $(k+1)$-node…
We define and study a class of (random) Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions. The constraints we consider encode, respectively, for hard mass-balance…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We prove that if A is a large random relational structure with at least one relation of arity at least 2 then the problem EXT(A) is almost surely NP-complete.
A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…
We systematically study the computational complexity of a broad class of computational problems in phylogenetic reconstruction. The class contains for example the rooted triple consistency problem, forbidden subtree problems, the quartet…
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…
To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…