TY - GEN

T1 - A dichotomy result for cyclic-order traversing games

AU - Chen, Yen Ting

AU - Tsai, Meng-Tsung

AU - Tsai, Shi-Chun

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - And phrases st-planar graphs

KW - Biconnectivity

KW - Fault-tolerant routing algorithms

KW - Software defined network

UR - http://www.scopus.com/inward/record.url?scp=85063674470&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2018.29

DO - 10.4230/LIPIcs.ISAAC.2018.29

M3 - Conference contribution

AN - SCOPUS:85063674470

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 29th International Symposium on Algorithms and Computation, ISAAC 2018

A2 - Lee, Der-Tsai

A2 - Liao, Chung-Shou

A2 - Hsu, Wen-Lian

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 29th International Symposium on Algorithms and Computation, ISAAC 2018

Y2 - 16 December 2018 through 19 December 2018

ER -