本研究探討高密度時間序列交通資訊的即時路徑規劃，在一個給定的路網中找到一條從起點到終點之最佳路徑，然而此路徑在現實情況可能會發生交通壅塞或事故並且造成長時間的延遲。從應用角度來看，本研究討論了在路網交通狀況動態變化之最佳路徑查詢問題。與之前的研究相比，我們設計了有效率的演算法來解決在不滿足先進先出條件下的時間序列交通資訊路網的最佳路徑問題。此外，對於高密度時間序列交通資訊的路網，我們提出了可以顯著減少計算負荷的資料結構。雖然在預先處理所得到之資料結構大小可能因為太大而不實用，但是此方法可以立即反映真實世界中的即時交通狀況變化。我們還提出了一些啟發式加速計算的方法，並且透過實驗證明了該即時近似最短路徑演算法非常接近該路網在知道所有交通資訊情況下的最短路徑(即最佳解)。

This study investigates the online route planning problem in time-dependent traffic networks. Given a road network, the problem involves planning a dynamic route as short as possible from a source to a destination, but possibly discovering online (real-time) traffic congestions or accidents, which may cause long delays. From a practical perspective, the problem discusses the shortestpath query problem with a set of dynamic changes that are subject to online traffic conditions. In comparison with prior work, we design efficient algorithms for solving this problem without the assumption that the given time-dependent networks satisfy the FIFO (First-In-First-Out) property. Moreover, we conduct empirical studies with high-density time-series traffic data and exploit data structures to significantly reduce computation loads. In fact, the size of the resulting sets of preprocessed data structures might be too heavy to be practical. Our approaches can immediately respond to online traffic changes, but in small real-world instances. We also propose some heuristics to speed up computation, and the experiments demonstrate the effectiveness of the proposed algorithms. In particular, the travel cost of the derived online near-shortest routes can be shown very close to that of the static (offline) time-dependent shortest paths in hindsight, where all traffic changes are known a priori.

摘要 I
Abstract II
誌謝 III
Contents IV
List of Figures and Tables V
1 Introduction 1
2 Preliminaries 7
2.1 Traffic Networks 7
2.2 Offline Routing 8
2.3 Online Routing 10
3 Non-FIFO Time-dependent Dijkstra’s Algorithm 12
4 Online Time-dependent Dijkstra’s Algorithm 16
4.1 Online Algorithm 16
4.2 Online Algorithm 17
5 Experimental Result 19
6 Conclusion and Future Work 22
References 23

[1] H. Bast, D. Delling, A.V. Goldberg, M. Mu¨ller-Hannemann, T. Pajor, P. Sanders, D. Wagner, R. Werneck. Route planning in transportation networks. Techical Report, MSR-TR-2014-4, (2014), Microsoft Research.

[2] G.V. Batz, D. Deling, P. Sanders, and C. Vetter. Time-Dependent Contrac-tion Hierarchies. In Proc the 11th Workshop on Algorithm Engineering and Experiments (ALENEX), (2009), pp. 97–105.

[3] G.V. Batz, R. Geisberger, S. Neubauer, and P. Sanders. Time-dependent contraction hierarchies and approximation. In Proc. International Symposium on Experimental Algorithms (SEA). LNCS 6049, (2010), pp. 166–177.

[4] G.V. Batz, R. Geisberger, P. Sanders, and C. Vetter. Minimum time-dependent travel times with contraction hierarchies. ACM Journal of Ex-perimental Algorithmics, (2013), 18(1), pp. 1–4.

[5] G.V. Batz and P. Sanders. Time-dependent route planning with generalized objective functions. In Proc. the 20th Annual European Symposium on Algo-rithms (ESA). LNCS 7501, (2012), pp. 169–180.

[6] R. Bauer, D. Delling, P. Sanders, D. Schieferdecker, D. Schultes, and D. Wagner. Combining hierarchical and goal-directed speed-up techniques for Dijkstra’s algorithm. ACM Journal of Experimental Algorithmics, (2010), 15, pp. 2–3.

[7] A. Borodin and R. El-Yaniv. Online computation and competitive analysis. Cambridge University Press, Cambridge, (1998).

[8] B.C. Dean. Shortest paths in FIFO time-dependent networks: Theory and algorithms. Technical report, (2004), Massachusetts Institute of Technology.

[9] D. Delling. Time-dependent SHARC-routing. Algorithmica, (2011), 60(1), pp. 60–94.

[10] D. Delling and D. Wagner. Time-dependent route planning. In Proc. Robust and Online Large-Scale Optimization: Models and Techniques for Transporta-tion Systems. LNCS 5868, (2009), pp. 207–230.

[11] D. Delling, P. Sanders, D. Schultes, and D. Wagner. Engineering Route Planning Algorithms. In Proc. Algorithmics of Large and Complex Networks. LNCS 5515, (2009), pp. 117–139.

[12] E. Demaine, Y. Huang, C.-S. Liao, and K. Sadakane. Canadians Should Travel Randomly. In Proc. the 41st International Colloquium on Automata, Lan-guages, and Programming (ICALP), LNCS 8572, (2014), pp. 380–391.

[13] P.A. Devijver and J. Kittler. Pattern recognition: a statistical approach. Prentice Hall, London, (1982).

[14] J. Dibbelt, B. Strasser, and D. Wagner. Customizable contraction hierarchies. In Proc. International Symposium on Experimental Algorithms (SEA). LNCS 8504, (2014), pp. 271–282.

[15] S.E. Dreyfus. An appraisal of some shortest-path algorithms. Operations Re-search, (1969), 17(3), pp.395–412.

[16] L. Foschini, J. Hershberger, and S. Suri. On the Complexity of Time-Dependent Shortest Paths. Algorithmica, (2014), 68(4), pp. 1075–1097.

[17] R. Geisberger, P. Sanders, D. Schultes, and D. Delling. Contraction hier-archies: Faster and simpler hierarchical routing in road networks. In Proc. International Symposium on Experimental Algorithms (SEA). LNCS 5038,(2008), pp. 319–333.

[18] R. Geisberger, P. Sanders, D. Schultes, and C. Vetter. Exact routing in large road networks using contraction hierarchies. Transportation Science, (2012), 46(3), pp. 388–404.

[19] S. Geisser. Predictive inference: An Introduction. Chapman and Hall, New York, (1993).

[20] D. Kehagias, T. Diamantopoulos. Analysis of the State-of-the-Art for Vehic-ular Traffic Prediction. Technical report, (2013), eCOMPASS-TR-035.

[21] V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. the 40th IEEE Symposium on Foundations of Computer Science (FOCS), (1999), pp. 81–90.

[22] M. Kobitzsch. An alternative approach to alternative routes: HiDAR. In Proc. the 21st Annual European Symposium on Algorithms (ESA). LNCS 8125, (2013), pp. 613–624.

[23] S. Kontogiannis, G. Michalopoulos, G. Papastavrou, A. Paraskevopoulos, D. Wagner, and C. Zaroliagis. Analysis and Experimental Evaluation of Time-Dependent Distance Oracles. the 17th Workshop on Algorithm Engineering and Experiments (ALENEX), (2015), pp. 147–158.

[24] S. Kontogiannis and C. Zaroliagis. Distance oracles for time-dependent net-works. In Proc. the 41st International Colloquium on Automata, Languages, and Programming (ICALP), LNCS 8572, (2014), pp. 713–725.

[25] R. Kohavi. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proc. International Joint Conference on Artificial Intelligence (IJCAI), (1995), pp. 1137–1145.

[26] C.-S. Liao and Y. Huang. Generalized Canadian Traveller Problems. Journal of Combinatorial Optimization, 29(4),(2013), pp. 701–712.

[27] C.-S. Liao and Y. Huang. The Covering Canadian Traveller Problem. Theo-retical Computer Science, 530(2014), pp. 80–88.

[28] F. Merz and P. Sanders. PReaCH: A fast lightweight reachability index us-ing pruning and contraction hierarchies. In Proc. the 22nd Annual European Symposium on Algorithms (ESA), LNCS 8737, (2014), pp. 701–712.

[29] G. Nannicini, D. Delling, L. Liberti, and D. Schultes. Bidirectional A∗ search for time-dependent fast paths. In Proc. International Symposium on Experi-mental Algorithms (SEA), LNCS 5038, (2008), pp. 334–346.

[30] A. Orda and R. Rom. Shortest-path and minimumdelay algorithms in net-works with time-dependent edge-length. Journal of the ACM, (1990), 37(3), pp.607–625.

[31] C.H. Papadimitriou and M. Yannakakis. Shortest paths without a map. The-oretical Computer Science, (1991), 84(1), pp. 127–150.

[32] A. Paraskevopoulos and C. Zaroliagis. Improved alternative route planning. In Proc. the 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS), (2014), pp. 108–122.

[33] P. Sanders and D. Schultes. Engineering fast route planning algorithms. In Proc. International Symposium on Experimental Algorithms (SEA), LNCS 4525, (2007), pp. 23–36.

[34] M. Thorup. Worst-case update times for fully dynamic all-pairs shortest paths. In Proc. the 37th Annual ACM Symposium on Theory of Computing (STOC), (2005), pp. 112–119.

[35] S. Westphal. A note on the k-Canadian traveller problem. Information Pro-cessing Letters, (2008), 106, pp. 87–89.