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Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…
Modern software systems are often highly configurable to tailor varied requirements from diverse stakeholders. Understanding the mapping between configurations and the desired performance attributes plays a fundamental role in advancing the…
Flexible graph connectivity is a new network design model introduced by Adjiashvili. It has seen several recent algorithmic advances. Despite these, the approximability even in the setting of a single-pair $(s,t)$ is poorly understood. In…
Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require…
Grasping in dynamic environments presents a unique set of challenges. A stable and reachable grasp can become unreachable and unstable as the target object moves, motion planning needs to be adaptive and in real time, the delay in…
This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
We present a geometric framework for filtered approximate nearest neighbor (ANN) search. Filtering a proximity graph by a metadata predicate produces a subgraph, a fiber, whose connectivity and geometry can differ sharply from the full…
We provide an up-to-date view of the structure of the energy landscape of the low autocorrelation binary sequences problem, a typical representative of the $NP$-hard class. To study the landscape features of interest we use the local optima…
The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature…
Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length $L$, an overview of…
With the rapid rise of neural architecture search, the ability to understand its complexity from the perspective of a search algorithm is desirable. Recently, Traor\'e et al. have proposed the framework of Fitness Landscape Footprint to…
Several approaches have been recently proposed for community search in bipartite graphs. These methods have shown promising results in identifying communities in real-world bipartite networks, such as social and biological networks. Given a…
Information technology has spread widely, and extraordinarily large amounts of data have been made accessible to users, which has made it challenging to select data that are in accordance with user needs. For the resolution of the above…
Since knowledge graphs (KGs) describe and model the relationships between entities and concepts in the real world, reasoning on KGs often correspond to the reachability queries with label and substructure constraints (LSCR). Specially, for…
Modern software systems are often highly configurable to tailor varied requirements from diverse stakeholders. Understanding the mapping between configurations and the desired performance attributes plays a fundamental role in advancing the…
Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a…
Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…