Surging e-commerce and global trade necessitate highly efficient cargo terminal operations. Modern automated terminals, crucial for supply chains, employ complex networks of static and movable equipment. This integration introduces a core challenge: movable equipment creates dynamic connectivity and state-dependent travel times, rendering classic shortest path algorithms based on static edge weights ineffective. Unlike typical time-dependent problems driven by external factors such as traffic congestion or fixed schedules, our dynamics stem from internal equipment state, presenting a unique optimization challenge. We address the problem of finding optimal cargo routes within these dynamic environments. We propose a novel approach by modeling the terminal as a cargo network, where virtual edges induced by movable equipment are explicitly materialised and edge costs reflect the status of the real-time equipment. We propose an efficient Dijkstra's-based algorithm to solve the cargo routing problem within this framework considering the system dynamics. The primary contributions of this paper are this novel modeling technique for dynamic terminals and the adapted algorithm for optimal routing, offering significant benefits for logistics optimization and automated warehouse design. Experimental results demonstrate that our approach significantly reduces cargo travel times compared to baseline methods, offering substantial improvements for logistics efficiency in automated terminals.

The Constrained Shortest Path (CSP) problem seeks to identify the shortest path between two vertices in a road network while adhering to a specific constraint on another criterion. Solving the CSP problem frequently entails navigating the two-criteria skyline path problem, which incurs a substantial computational expense in large road networks. The primary challenge lies in handling a vast quantity of partial skyline paths, which often hinders index-based solutions from accurately determining the skyline paths. This paper introduces a-FHL, a practical approximation method designed to circumvent the costly skyline path search and hasten computation on skyline path indexing. a-FHL uses tree decomposition to hierarchically assign approximation ratios, thereby facilitating effective pruning within the labelling index. Moreover, we devise various strategies to allocate approximation ratios and an efficient approximation concatenation method to respond to the approximate CSP queries via the a-FHL index. Our method culminates in swift index construction and efficient query response. Comprehensive exper-iments conducted on real-world road networks substantiate the superiority of our approach over contemporary solutions

Multi-Constraint Shortest Path ( MCSP ) generalizes the classic shortest path from single to multiple criteria such that more personalized needs can be satisfied. However, MCSP query is essentially a high-dimensional skyline problem and thus time-consuming to answer. Although the current Forest Hop Labeling (FHL) index can answer MCSP efficiently, it takes a long time to construct and lacks the flexibility to handle arbitrary criteria combinations. In this paper, we propose a skyline-cube-based FHL index that can handle the flexible MCSP efficiently. Firstly, we analyze the relation between low and high-dimensional skyline paths theoretically and use a cube to organize them hierarchically. After that, we propose methods to derive the high-dimensional path from the lower ones, which can adapt to the flexible scenario naturally and reduce the expensive high dimensional path concatenation. Then we introduce efficient methods for both single and multi-hop cube concatenations and propose pruning methods to further alleviate the computation. Finally, we improve the FHL structure with lower height for faster construction and query. Experiments on real-life road networks demonstrate the superiority of our method over the state-of-the-art.

The Constrained Shortest Path (CSP) problem aims to find the shortest path between two nodes in a road network subject to a given constraint on another attribute. It is typically processed as a skyline path problem on the two attributes, resulting in very high computational cost which can be prohibitive for large road networks. The main bottleneck is to deal with a large amount of partial skyline paths, which further makes the existing index-based methods incapable to obtain the complete exact skyline paths. In this paper, we propose a novel skyline path concatenation approach to avoid the expensive skyline path search, which is then used to efficiently construct a 2-hop labeling index for the CSP queries. Specifically, a rectangle-based technique is designed to prune the concatenation space from multiple hops, and a constraint pruning method is used to further speed up the CSP query processing. To further scale up to larger networks, we propose a novel forest hop labeling that constructs labels from different partitions in parallel. Our approach is the first method that can achieve both accuracy and efficiency for CSP query answering. Extensive experiments on real-life road networks demonstrate that our method outperforms the state-of-the-art CSP solutions by several orders of magnitude.