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We study community search when each member has its own tolerance for differences in position, as when members of a group interact repeatedly and influence one another. A latitude-consistent community (LCC) contains the query vertex, is connected, has minimum degree at least k, and bounds its diameter by the smallest member tolerance. The bound is exactly the condition under which every interaction in a connected closed group stays accepted under bounded-confidence dynamics for every choice of positive weights. It also prevents rejection under social-judgment dynamics, whereas the pairwise condition and other natural relaxations preserve neither guarantee. Finding a maximum LCC is NP-hard even in the plane, and with unbounded dimension, deciding whether an LCC exists is NP-complete for every fixed k>=2. LatSweep fixes the answer's smallest tolerance and turns the coupled bound into a best-first sweep over candidate thresholds, yielding an exact branch-and-bound algorithm, a (1,2)-bicriteria approximation and two feasible heuristics. Across eight graphs with up to 1.8 billion edges, six with synthetic positions and tolerances, the exact algorithm proves optimality on all but 9 of 3,700 efficiency queries; in a shared implementation on two large graphs, its branch-and-bound solver proves more queries than a reimplemented maximum-(k,r)-core algorithm, a mixed-integer program and CP-SAT. In simulations of closed groups, LCC groups keep every accepted interaction under uneven influence, whereas 3-40% of pairwise-compatible groups lose some. On three location-based networks, tolerance-agnostic groups often place another member's home beyond a member's estimated travel radius. Enforcing every member's tolerance causes no measurable loss of co-visits relative to spatial communities of the same size. Relative to the larger pairwise-compatible groups, it can cause a size-adjusted loss.

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.