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We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…
We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…
We study the parameterized complexity of the following factorization problem: given elements $a,a_1, \ldots, a_m$ of a monoid and a parameter $k$, can $a$ be written as the product of at most (or exactly) $k$ elements from $a_1, \ldots,…
We investigate {\em multidimensional covering mechanism-design} problems, wherein there are $m$ items that need to be covered and $n$ agents who provide covering objects, with each agent $i$ having a private cost for the covering objects he…
We study the problem Symmetric Directed Multicut from a parameterized complexity perspective. In this problem, the input is a digraph $D$, a set of cut requests $C=\{(s_1,t_1),\ldots,(s_\ell,t_\ell)\}$ and an integer $k$, and the task is to…
We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed…
The k-means problem consists of finding k centers in the d-dimensional Euclidean space that minimize the sum of the squared distances of all points in an input set P to their closest respective center. Awasthi et. al. recently showed that…
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
We study a variant of Set Cover where each element of the universe has some demand that determines how many times the element needs to be covered. Moreover, we examine two generalizations of this problem when a set can be included multiple…
Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
Given a simple undirected graph $G$, a quasi-clique is a subgraph of $G$ whose density is at least $\gamma$ $(0 < \gamma \leq 1)$. Finding a maximum quasi-clique has been addressed from two different perspectives: $i)$ maximizing vertex…
While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this…
We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.