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We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be…
In this work, we address the task of natural image generation guided by a conditioning input. We introduce a new architecture called conditional invertible neural network (cINN). The cINN combines the purely generative INN model with an…
We consider the algorithmic problem of generating each subset of $[n]:=\{1,2,\ldots,n\}$ whose size is in some interval $[k,l]$, $0\leq k\leq l\leq n$, exactly once (cyclically) by repeatedly adding or removing a single element, or by…
We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in…
Coroutines are non-preemptive concurrent subroutines that, unlike preemptive threads, voluntarily transfer control between each others. Introduced in the 60s before loosing in popularity in the 80s, they have seen a regain of interest in…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
The cycles are the only $2$-connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer $k\ge 3$ there exists a unique graph $G$ satisfying the following conditions:…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm…
We consider the following combinatorial question. Let $$ S_0 \subset S_1 \subset S_2 \subset ...\subset S_m $$ be nested sets, where #$(S_i) = i$. A move consists of altering one of the sets $S_i$, $1 \le i \le m-1$, in a manner so that the…
In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear…
We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search…
Inferring objects and their relationships from an image in the form of a scene graph is useful in many applications at the intersection of vision and language. We consider a challenging problem of compositional generalization that emerges…
A major archetype of artificial intelligence is developing algorithms facilitating temporal efficiency and accuracy while boosting the generalization performance. Even with the latest developments in machine learning, a key limitation has…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…