Kam-Fung Cheung | Searcharxiv

arXiv2026

Urban transit network design using spanning tree: A case study of Canberra transit network

Transit network design plays an important role in public transport. With the simplicity of spanning tree, this paper adopts the concept of spanning tree to help (re-)design a public transit network that addresses passenger utility by minimizing the total passenger-kilometers, which can be formulated as a mixed-integer optimization model. However, searching for an optimal minimum passenger-kilometer spanning tree is intractable for a large network. This paper proposes a tabu search based heuristic to quickly output a promising spanning tree. The efficacy of the proposed tabu search based heuristic is verified using the Canberra bus network data. With the flexibility of the proposed tabu search heuristic and the efficiency of the transit system, this paper proposes a greedy algorithm to relax the number of links constraint to add more links that can further minimize the total passenger-kilometers. With the case study of Canberra transit network, this paper provides implications to policy makers to further improve the design of a public transit network.

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arXiv2018

Phase Retrieval via Sensor Network Localization

The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast theoretical and algorithmic literature on the latter to tackle the former. Leveraging this connection, we develop a two-stage algorithm for phase retrieval that can provably recover the desired signal. In both sparse and dense settings, our proposed algorithm improves upon prior approaches simultaneously in the number of required measurements for recovery and the reconstruction time. We present numerical results to corroborate our theory and to demonstrate the efficiency of the proposed algorithm. As a side result, we propose a new form of phase retrieval problem and connect it to the complex rigidity theory proposed by Gortler and Thurston.

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