Discrete Mathematics - Topics on domination
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Routing with guaranteed delivery in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Geometric ad-hoc routing: of theory and practice
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
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DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Practical, distributed network coordinates
ACM SIGCOMM Computer Communication Review
Virtual coordinates for ad hoc and sensor networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Virtual coordinates for ad hoc and sensor networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Sextant: a unified node and event localization framework using non-convex constraints
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Evolutionary algorithms for the self-organized evolution of networks
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Deterministic boundary recognition and topology extraction for large sensor networks
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Theoretical aspects of connectivity-based multi-hop positioning
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Distributed localization using noisy distance and angle information
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Hole detection or: "how much geometry hides in connectivity?"
Proceedings of the twenty-second annual symposium on Computational geometry
Determining a sequence of stable multicast Steiner trees in mobile ad hoc networks
Proceedings of the 44th annual Southeast regional conference
Wireless localization using self-organizing maps
Proceedings of the 6th international conference on Information processing in sensor networks
Local solutions for global problems in wireless networks
Journal of Discrete Algorithms
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Cross-layer latency minimization in wireless networks with SINR constraints
Proceedings of the 8th ACM international symposium on Mobile ad hoc networking and computing
On Boundary Recognition without Location Information in Wireless Sensor Networks
IPSN '08 Proceedings of the 7th international conference on Information processing in sensor networks
An algorithmic approach to geographic routing in ad hoc and sensor networks
IEEE/ACM Transactions on Networking (TON)
Ad hoc networks beyond unit disk graphs
Wireless Networks
Modelling gateway placement in wireless networks: geometric k-centres of unit disc graphs
Proceedings of the fifth international workshop on Foundations of mobile computing
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
Localization and routing in sensor networks by local angle information
ACM Transactions on Sensor Networks (TOSN)
Local PTAS for Dominating and Connected Dominating Set in Location Aware Unit Disk Graphs
Approximation and Online Algorithms
Algorithms for ad hoc and sensor networks
Computer Communications
On boundary recognition without location information in wireless sensor networks
ACM Transactions on Sensor Networks (TOSN)
Sensor networks continue to puzzle: selected open problems
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Algorithms for sensor and ad hoc networks: advanced lectures
Algorithms for sensor and ad hoc networks: advanced lectures
Deterministic robot-network localization is hard
IEEE Transactions on Robotics
Theoretical Computer Science
On the topologies of local minimum spanning trees
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
Geometric routing without geometry
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Wireless networking: graph theory unplugged
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Maximum stability data gathering trees for mobile sensor networks
International Journal of Mobile Network Design and Innovation
International Journal of Interdisciplinary Telecommunications and Networking
Broadcasting in logarithmic time for ad hoc network nodes on a line using mimo
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
International Journal of Mobile Network Design and Innovation
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Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a non-approximability result for the problem of embedding a given unit disk graph. Particularly, we show that if non-neighboring nodes are not allowed to be closer to each other than distance 1, then two neighbors can be as far apart as √3/2 - ε, where ε goes to 0 as n goes to infinity, unless P=NP. We further show that finding a realization of a d-quasi unit disk graph with d ≥ 1/√2 is NP-hard.