Algorithmic and complexity issues of robot motion in an uncertain environment
Journal of Complexity
Robot navigation with range queries
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
Reconfiguring Arrays with Faults Part I: Worst-Case Faults
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
IEEE Transactions on Parallel and Distributed Systems
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Asymptotically optimal geometric mobile ad-hoc routing
DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
SIAM Journal on Computing
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Extended Minimal Routing in 2-D Meshes with Faulty Blocks
ICDCSW '02 Proceedings of the 22nd International Conference on Distributed Computing Systems
On-line Searching and Navigation
Developments from a June 1996 seminar on Online algorithms: the state of the art
Competitive Time and Traffic Analysis of Position-Based Routing using a Cell Structure
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 12 - Volume 13
A survey on position-based routing in mobile ad hoc networks
IEEE Network: The Magazine of Global Internetworking
ACM SIGACT News
Online multi-path routing in a maze
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We consider the problem of routing a message in a mesh network with faulty nodes. The number and positions of faulty nodes is unknown. It is known that a flooding strategy like expanding ring search can route a message in the minimum number of steps h while it causes a traffic (i.e. the total number of messages) of ${\mathcal O}(h^{2})$. For optimizing traffic a single-path strategy is optimal producing traffic ${\mathcal O}(p + h)$, where p is the perimeter length of the barriers formed by the faulty nodes. Therefore, we define the comparative traffic ratio as a quotient over p+h and the competitive time ratio as a quotient over h. Optimal algorithms with constant ratios are known for time and traffic, but not for both. We are interested in optimizing both parameters and define the combined comparative ratio as the maximum of competitive time ratio and comparative traffic ratio. Single-path strategies using the right-hand rule for traversing barriers as well as multi-path strategies like expanding ring search have a combined comparative ratio of Θ(h). It is an open question whether there exists an online routing strategy optimizing time and traffic for meshes with an unknown set of faulty nodes. We present an online strategy for routing with faulty nodes providing sub-linear combined comparative ratio of $h^{{\mathcal O}(\sqrt{\frac{{\rm log log}h}{{\rm log}h}})}$.