Advancements in mobility services, navigation systems, and smart transportation technologies have made it possible to collect large amounts of path data. Modeling the distribution of this path data, known as the Path Generation (PG) problem, is crucial for understanding urban mobility patterns and developing intelligent transportation systems. Recent studies have explored using diffusion models to address the PG problem due to their ability to capture multimodal distributions and support conditional generation. A recent work devises a diffusion process explicitly in graph space and achieves state-of-the-art performance. However, this method suffers a high computation cost in terms of both time and memory, which prohibits its application. In this paper, we analyze this method both theoretically and experimentally and find that the main culprit of its high computation cost is its explicit design of the diffusion process in graph space. To improve efficiency, we devise a Latent-space Path Diffusion (LPD) model, which operates in latent space instead of graph space. Our LPD significantly reduces both time and memory costs by up to 82.8% and 83.1%, respectively. Despite these reductions, our approach does not suffer from performance degradation. It outperforms the state-of-the-art method in most scenarios by 24.5%~34.0%.

This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a robot that must locate a hidden target in an environment that consists of a set of concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using a common approach.