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Furthermore, we denote by δ + (S) = (P2) for all v ∈ V (TD ) \ {r}, there exists a directed {(i, j) ∈ A ∪ Ar | i ∈ S, j ∈ V \ S} and δ − (S) = {(i, j) ∈ path r → v in TD , and A ∪ Ar | i ∈ V \ S, j ∈ S} the outgoing and ingoing edges of a set S, respectively. We can give the following (P3) for all v ∈ V (TD ) \ {r}, v has in-degree 1 in TD . 1) a∈A of G by two arcs (i, j) and (j, i), introduce an artificial root vertex r and connect r to every node in V . 2) x(δ − (S)) ≥ yv ∀S ⊆ V \ {r}, ∀v ∈ S A = {(i, j), (j, i) | {i, j} ∈ E} and Ar = {(r, j) | j ∈ V }.

Delling and D. Wagner. Landmark-Based Routing in Dynamic Graphs. In Demetrescu [8], pages 52–65. [8] C. Demetrescu, editor. Proceedings of the 6th Workshop on Experimental Algorithms (WEA’07), volume 4525 of Lecture Notes in Computer Science. Springer, June 2007. [9] C. Demetrescu, A. V. Goldberg, and D. S. Johnson, editors. 9th DIMACS Implementation Challenge Shortest Paths, November 2006. [10] E. W. Dijkstra. A Note on Two Problems in Connexion with Graphs. Numerische Mathematik, 1:269–271, 1959.

D. Schultes and P. Sanders. Dynamic Highway-Node Routing. In Demetrescu [8], pages 66–79. R. D. Team. R: A Language and Environment for Statistical Computing, 2004. D. Wagner and T. Willhalm. Speed-Up Techniques for Shortest-Path Computations. In Proceedings of the 24th International Symposium on Theoretical Aspects of Computer Science (STACS’07), Lecture Notes in Computer Science, pages 23–36. Springer, February 2007. [34] D. Wagner, T. Willhalm, and C. Zaroliagis. Geometric Containers for Efficient Shortest-Path Computation.

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