# The Thinnest Path Problem

@article{Gao2015TheTP, title={The Thinnest Path Problem}, author={Jianhang Gao and Qing Zhao and Ananthram Swami}, journal={IEEE/ACM Transactions on Networking}, year={2015}, volume={23}, pages={1176-1189} }

We formulate and study the thinnest path problem for secure communication in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission powers. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms…

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## References

SHOWING 1-10 OF 28 REFERENCES

Secluded Connectivity Problems

- Mathematics, Computer ScienceESA
- 2013

It is shown that on unweighted undirected n-node graphs, the problem of finding the minimum exposure path connecting a given pair of vertices is strongly inapproximable, but is approximable with ratio \(\sqrt{\Delta }+3\), where Δ is the maximum degree in the graph.

A robust interference model for wireless ad-hoc networks

- Computer Science19th IEEE International Parallel and Distributed Processing Symposium
- 2005

This paper presents a receiver-centric interference model featuring two main advantages over previous work: first, it reflects the fact that interference occurs at the intended receiver of a message, and second, the presented interference measure is robust with respect to addition or removal of single network nodes.

Minimizing Interference of a Wireless Ad-Hoc Network in a Plane

- MathematicsALGOSENSORS
- 2006

A method based on quad-tree decomposition and bucketing is given that has another provable interference bound in terms of the ratio of the minimum distance to the radius of a uniform-radius ad-hoc network.

Dynamic Shortest Path Algorithms for Hypergraphs

- Computer ScienceIEEE/ACM Transactions on Networking
- 2015

These two algorithms are the first to address the fully dynamic shortest path problem in a general hypergraph and complement each other by partitioning the application space based on the nature of the change dynamics and the type of the hypergraph.

Optimal Traversal of Directed Hypergraphs

- Computer Science
- 1992

This paper considers the problem of nding minimal hyperpaths according to several measures and describes eecient algorithms and data structures which can be used with any value-based measure function, since it appears in parametric form.

Graphs and Hypergraphs

- Mathematics
- 2021

Independence densities of hypergraphs We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence…

A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP

- MathematicsSTOC '97
- 1997

A new low-degree-test is introduced, one that uses the restriction of low- degree polynomials to planes rather than the restriction to lines, and enables us to prove a low-error characterization of NP in terms of PCP.

Beyond graphs: Capturing groups in networks

- Computer Science2011 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)
- 2011

It is shown that a number of problems within social and communications networks such as network-wide broadcast and collaborative teams can be elegantly captured using simplicial complexes in a way that is not possible with graphs.