Approximating the minimum maximal independence number
Information Processing Letters
Explaining type errors in polymorphic languages
ACM Letters on Programming Languages and Systems (LOPLAS)
Finding Regular Simple Paths in Graph Databases
SIAM Journal on Computing
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ACM SIGACT News
Regular path queries with constraints
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Graph-theoretic methods in database theory
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Formal-Language-Constrained Path Problems
SIAM Journal on Computing
Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A high-throughput path metric for multi-hop wireless routing
Proceedings of the 9th annual international conference on Mobile computing and networking
Routing in multi-radio, multi-hop wireless mesh networks
Proceedings of the 10th annual international conference on Mobile computing and networking
On Two Problems in the Generation of Program Test Paths
IEEE Transactions on Software Engineering
Information and Computation
Quickest path distances on context-free labeled graphs
ISP'07 Proceedings of the 6th WSEAS international conference on Information security and privacy
A trichotomy for regular simple path queries on graphs
Proceedings of the 32nd symposium on Principles of database systems
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Metrics to assess the cost of paths through networks are critical to ensuring the efficiency of network routing. This is particularly true in multi-radio multi-hop wireless networks. Effective metrics for these networks must measure the cost of a wireless path based not only on traditional measures such as throughput, but also on the distribution of wireless channels used. In this paper, we argue that routing metrics over such networks may be viewed as a class of existing shortest path problems, the formal language constrained path problems. On this basis, we describe labeled path problems corresponding to two multi-radio wireless routing metrics: Weighted Cumulative Expected Transmission Time (WCETT), developed by Draves et al., and Metric for Interference and Channel-switch (MIC), developed by Yang et al. For the first, we give a concise proof that calculating shortest WCETT paths is strongly NP-Complete for a variety of graph classes. We also show that the existing heuristic given by Draves et al. is an approximator. For the second, we show that calculating loop-free (simple) shortest MIC paths is NP-Complete, and additionally show that the optimization version of the problem is NPO PB-Complete. This result implies that shortest simple MIC paths are only poorly approximable in the worst case. Furthermore, we demonstrate how the polynomial-time algorithm for shortest MIC paths is derivable from an existing language constrained shortest path algorithm. We use this as a basis to exhibit the general utility of viewing multi-channel wireless routing metrics as labeled graph problems, and discuss how a class of related polynomial-time computable metrics are derivable from this algorithm.