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


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 languageEnglish
Title of host publication29th International Symposium on Algorithms and Computation, ISAAC 2018
EditorsDer-Tsai Lee, Chung-Shou Liao, Wen-Lian Hsu
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770941
StatePublished - 1 Dec 2018
Event29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan
Duration: 16 Dec 201819 Dec 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference29th International Symposium on Algorithms and Computation, ISAAC 2018
CityJiaoxi, Yilan


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

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