However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact--implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

The appendix is organized as follows: Appendix A: In this section, we prove IS functions are XOS. Appendix B: In this section, we formally prove our main results in Section 3. Appendix C: In this section, we formally prove our main results in Section 4. Appendix D: In this section, we introduce a milder efficiency requirement IO and study its compatibility with EF1. Appendix E: In this section, we discuss our experiments in more details. Regarding agents' utilities, FISP contains three cases, from the most special to the most general: Unweighted: u J, i.e., agents have unary utility for jobs. J, i.e., all jobs have unit processing time.

We initiate the study of a variant of the classic online speed scaling problem, in which machine learning predictions about the future can be integrated naturally.

In Multiagent Path Finding (MAPF), the goal is to compute efficient, collision-free paths for multiple agents navigating a network from their sources to targets, minimizing the schedule's makespan-the total time until all agents reach their destinations. We introduce a new variant that formally models scenarios where some agents may experience delays due to malfunctions, posing significant challenges for maintaining optimal schedules. Recomputing an entirely new schedule from scratch after each malfunction is often computationally infeasible. To address this, we propose a framework for dynamic schedule adaptation that does not rely on full replanning. Instead, we develop protocols enabling agents to locally coordinate and adjust their paths on the fly. We prove that following our primary communication protocol, the increase in makespan after k malfunctions is bounded by k additional turns, effectively limiting the impact of malfunctions on overall efficiency. Moreover, recognizing that agents may have limited computational capabilities, we also present a secondary protocol that shifts the necessary computations onto the network's nodes, ensuring robustness without requiring enhanced agent processing power. Our results demonstrate that these protocols provide a practical, scalable approach to resilient multiagent navigation in the face of agent failures.

We present a heuristic algorithm for solving the problem of scheduling plans of tasks. The plans are ordered vectors of tasks, and tasks are basic operations carried out by resources. Plans are tied by temporal, precedence and resource constraints that makes the scheduling problem hard to solve in polynomial time. The proposed heuristic, that has a polynomial worst-case time complexity, searches for a feasible schedule that maximize the number of plans scheduled, along a fixed time window, with respect to temporal, precedence and resource constraints.

The Young Physicists Tournament is an established team-oriented scientific competition between high school students from 37 countries on 5 continents. The competition consists of scientific discussions called Fights. Three or four teams participate in each Fight, each of whom presents a problem while rotating the roles of Presenter, Opponent, Reviewer, and Observer among them. The rules of a few countries require that each team announce in advance 3 problems they will present at the national tournament. The task of the organizers is to choose the composition of Fights in such a way that each team presents each of its chosen problems exactly once and within a single Fight no problem is presented more than once. Besides formalizing these feasibility conditions, in this paper we formulate several additional fairness conditions for tournament schedules. We show that the fulfillment of some of them can be ensured by constructing suitable edge colorings in bipartite graphs. To find fair schedules, we propose integer linear programs and test them on real as well as randomly generated data.