Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in O(log n) flips) for general arboricity and beat it for either constant or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case O(1) and O(sqrt(log n)) flips nearly matching degree bounds to their respective amortized solutions.
Original language
English
Title of host publication
28th International Symposium on Algorithms and Computation (ISAAC 2017)
Editors
Yoshio Okamoto , Takeshi Tokuyama
Number of pages
11
Publisher
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
28th International Symposium on Algorithms and Computation - Cape Panwa Hotel, Phuket, Thailand Duration: 9 Dec 2017 → 12 Dec 2017 Conference number: 28 https://saki.siit.tu.ac.th/isaac2017/
Conference
Conference
28th International Symposium on Algorithms and Computation