Abstract
The setting for the online transportation problem is a metric space $M$, populated by $m$ parking garages of varying capacities. Over time cars arrive in $M$, and must be irrevocably assigned to a parking garage upon arrival in a way that respects the garage capacities. The objective is to minimize the aggregate distance traveled by the cars. In 1998, Kalyanasundaram and Pruhs conjectured that there is a $(2m-1)$-competitive deterministic algorithm for the online transportation problem, matching the optimal competitive ratio for the simpler online metric matching problem. Recently, Harada and Itoh presented the first $O(m)$-competitive deterministic algorithm for the online transportation problem. Our contribution is an alternative algorithm design and analysis that we believe is simpler.

Abstract
Premium air travel is often associated with a disproportionately large carbon emissions footprint. This association reflects the increased space and amenities typically found in premium cabins that existing discourse suggests makes their carriage more fuel, and consequently carbon, intensive. One increasingly popular solution is disincentivizing the use of premium cabins in favor of all-economy cabins. How effective might such a policy be. To what extent. And how may the revenue impact affect travelers. We address these questions by leveraging an empirical model that integrates cabin configuration data, fuel burn profiles across various aircraft types, and multi-month airfare datasets. Our findings are threefold. First, we find that favoring entirely foregoing premium travel classes can reduce per-passenger emissions by between 8.1 and 21.5 percent, the precise figure varying based on the type of aircraft and aircraft stage length involved. Second, we observe that these emissions reductions are far less assured on a per-flight and a lifespan basis. Here, an all-economy configuration can reduce emissions by 0.45 percent or increase emissions by as much as 1.43 percent. Third, we enumerate pronounced revenue consequences associated with an all-economy configuration. This configuration produces aggregate revenue declines of between 4.92 and 23.1 percent, necessitating airfare increases of between 6 and 30 percent to maintain baseline revenue. This increase risks imposing a profound and regressive economic burden on working-class travelers who exhibit markedly higher price elasticities of demand compared to their wealthier counterparts and highlights the cross-subsidization airlines leverage to ensure the accessibility of air travel.

Abstract
We consider the problem of routing for logistics purposes, in a contested environment where an adversary attempts to disrupt the vehicle along the chosen route. We construct a game-theoretic model that captures the problem of optimal routing in such an environment. While basic robust deterministic routing plans are already challenging to devise, they tend to be predictable, which can limit their effectiveness. By introducing calculated randomness via modeling the route planning process as a two-player zero-sum game, we compute immediately deployable plans that are diversified and harder to anticipate. Although solving the game exactly is intractable in theory, our use of the double-oracle framework enables us to achieve computation times on the order of seconds, making the approach operationally viable. In particular, the framework is modular enough to accommodate specialized routing algorithms as oracles. We evaluate our method on real-world scenarios, showing that it scales effectively to realistic problem sizes and significantly benefits from explicitly modeling the adversary's capabilities, as demonstrated through ablation studies and comparisons with baseline approaches.

Abstract
We consider the problem of minimizing the worst-case search time for a hidden point target in the plane using multiple mobile agents of differing speeds, all starting from a common origin. The search time is normalized by the target's distance to the origin, following the standard convention in competitive analysis. The goal is to minimize the maximum such normalized time over all target locations, the search cost. As a base case, we extend the known result for a single unit-speed agent, which achieves an optimal cost of about $\mathcal{U}_1 = 17.28935$ via a logarithmic spiral, to $n$ unit-speed agents. We give a symmetric spiral-based algorithm where each agent follows a logarithmic spiral offset by equal angular phases. This yields a search cost independent of which agent finds the target. We provide a closed-form upper bound $\mathcal{U}_n$ for this setting, which we use in our general result. Our main contribution is an upper bound on the worst-case normalized search time for $n$ agents with arbitrary speeds. We give a framework that selects a subset of agents and assigns spiral-type trajectories with speed-dependent angular offsets, again making the search cost independent of which agent reaches the target. A corollary shows that $n$ multi-speed agents (fastest speed 1) can beat $k$ unit-speed agents (cost below $\mathcal{U}_k$) if the geometric mean of their speeds exceeds $\mathcal{U}_n / \mathcal{U}_k$. This means slow agents may be excluded if they lower the mean too much, motivating non-spiral algorithms. We also give new upper bounds for point search in cones and conic complements using a single unit-speed agent. These are then used to design hybrid spiral-directional strategies, which outperform the spiral-based algorithms when some agents are slow. This suggests that spiral-type trajectories may not be optimal in the general multi-speed setting.

Abstract
Route recommendation (RR) is a core task of route planning in the Amap app, with the goal of recommending the optimal route among candidate routes to users. Unlike traditional recommendation methods, insights into the local quality of routes and comparisons between candidate routes are crucial for enhancing recommendation performance but often overlooked in previous studies. To achieve these, we propose a novel model called Comprehensive Comparison Network (CCN). CCN not only uses query-level features (e.g. user features) and item-level features (e.g. route features, item embedding) that are common in traditional recommendations, but also introduces comparison-level features which describe the non-overlapping segments between different routes to capture the local quality of routes. The key component Comprehensive Comparison Block (CCB) in CCN is designed to enable comparisons between routes. CCB includes a Comprehensive Comparison Operator (CCO) and a multi-scenario MLP, which can update the representations of candidate routes based on a comprehensive comparison. By stacking multiple CCBs, CCN can determine the final scores of candidate routes and recommend the optimal one to the user. Additionally, since routes directly affect the costs and risks experienced by users, the RR model must be interpretable for online deployment. Therefore, we designed an interpretable pair scoring network to achieve interpretability. Both offline and online experiments demonstrate that CCN significantly improves RR performance and exhibits strong interpretability. CCN has been fully deployed in the Amap app for over a year, providing stable and optimal benefits for route recommendations.

Abstract
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables fast and scalable computation of distances, barycenters, and kernels for probability measures, while retaining rich geometric structure. This paper provides a comprehensive review of SOT, covering its mathematical foundations, methodological advances, computational methods, and applications. We discuss key concepts of OT and one-dimensional OT, the role of tools from integral geometry such as Radon transform in projecting measures, and statistical techniques for estimating sliced distances. The paper further explores recent methodological advances, including non-linear projections, improved Monte Carlo approximations, statistical estimation techniques for one-dimensional optimal transport, weighted slicing techniques, and transportation plan estimation methods. Variational problems, such as minimum sliced Wasserstein estimation, barycenters, gradient flows, kernel constructions, and embeddings are examined alongside extensions to unbalanced, partial, multi-marginal, and Gromov-Wasserstein settings. Applications span machine learning, statistics, computer graphics and computer visions, highlighting SOT's versatility as a practical computational tool. This work will be of interest to researchers and practitioners in machine learning, data sciences, and computational disciplines seeking efficient alternatives to classical OT.

Abstract
Personalized text-to-image generation aims to synthesize novel images of a specific subject or style using only a few reference images. Recent methods based on Low-Rank Adaptation (LoRA) enable efficient single-concept customization by injecting lightweight, concept-specific adapters into pre-trained diffusion models. However, combining multiple LoRA modules for multi-concept generation often leads to identity missing and visual feature leakage. In this work, we identify two key issues behind these failures: (1) token-wise interference among different LoRA modules, and (2) spatial misalignment between the attention map of a rare token and its corresponding concept-specific region. To address these issues, we propose Token-Aware LoRA (TARA), which introduces a token mask to explicitly constrain each module to focus on its associated rare token to avoid interference, and a training objective that encourages the spatial attention of a rare token to align with its concept region. Our method enables training-free multi-concept composition by directly injecting multiple independently trained TARA modules at inference time. Experimental results demonstrate that TARA enables efficient multi-concept inference and effectively preserving the visual identity of each concept by avoiding mutual interference between LoRA modules. The code and models are available at https://github.com/YuqiPeng77/TARA.