A dichotomy result for cyclic-order traversing games

Yen Ting Chen, Meng-Tsung Tsai, Shi-Chun Tsai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Traversing game is a two-person game played on a connected undirected simple graph with a source node and a destination node. A pebble is placed on the source node initially and then moves autonomously according to some rules. Alice is the player who wants to set up rules for each node to determine where to forward the pebble while the pebble reaches the node, so that the pebble can reach the destination node. Bob is the second player who tries to deter Alice's effort by removing edges. Given access to Alice's rules, Bob can remove as many edges as he likes, while retaining the source and destination nodes connected. Under the guide of Alice's rules, if the pebble arrives at the destination node, then we say Alice wins the traversing game; otherwise the pebble enters an endless loop without passing through the destination node, then Bob wins. We assume that Alice and Bob both play optimally. We study the problem: When will Alice have a winning strategy? This actually models a routing recovery problem in Software Defined Networking in which some links may be broken. In this paper, we prove a dichotomy result for certain traversing games, called cyclic-order traversing games. We also give a linear-time algorithm to find the corresponding winning strategy, if one exists.

Original language English 29th International Symposium on Algorithms and Computation, ISAAC 2018 Der-Tsai Lee, Chung-Shou Liao, Wen-Lian Hsu Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 9783959770941 https://doi.org/10.4230/LIPIcs.ISAAC.2018.29 Published - 1 Dec 2018 29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, TaiwanDuration: 16 Dec 2018 → 19 Dec 2018

Publication series

Name Leibniz International Proceedings in Informatics, LIPIcs 123 1868-8969

Conference

Conference 29th International Symposium on Algorithms and Computation, ISAAC 2018 Taiwan Jiaoxi, Yilan 16/12/18 → 19/12/18

Keywords

• And phrases st-planar graphs
• Biconnectivity
• Fault-tolerant routing algorithms
• Software defined network