ABSTRACT
The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ε > 0, the labeling scheme stores an O(1+α-1)2α log2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in time polynomial in the length of the labels, a 1+ε stretch approximation for the distance between s and t in the graph GF. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ε for graphs of bounded doubling dimension.
- Ittai Abraham and Cyril Gavoille. Object location using path separators. In 25th ACM Symp. on Principles of Distributed Computing (PODC), 188--197, 2006. Google ScholarDigital Library
- Ittai Abraham, Cyril Gavoille, Andrew V. Goldberg, and Dahlia Malkhi. Routing in networks with low doubling dimension. In 26th Int. Conf. on Distributed Computing Systems (ICDCS), IEEE , 2006. Google ScholarDigital Library
- Aaron Bernstein and David Karger. A nearly optimal oracle for avoiding failed vertices and edges. In 41st ACM Symp. on Theory of Computing (STOC), 101--110, 2009. Google ScholarDigital Library
- Bruno Courcelle, Cyril Gavoille, Mamadou Mustapha Kanté, and David Andrew Twigg. Connectivity check in 3-connected planar graphs with obstacles. In Int. Conf. on Topological & Geometric Graph Theory, volume 31, 151--155. Electronic Notes in Discrete Mathematics, 2008.Google ScholarCross Ref
- Shiri Chechik, Michael Langberg, David Peleg, and Liam Roditty. f-sensitivity distance oracles and routing schemes. Unpublished manuscript, 2009.Google Scholar
- Bruno Courcelle and David Andrew Twigg. Compact forbidden-set routing. In 24th Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 4393, 37--48. SV, 2007. Google ScholarDigital Library
- Michael Dom. Compact routing. In Algorithms for Sensor and Ad Hoc Networks, LNCS 4621,187--202. SV, 2007.Google Scholar
- Ran Duan and Seth Pettie. Dual-failure distance and connectivity oracles. In 20nd Symp. on Discrete Algorithms (SODA), 506--515. ACM-SIAM, 2009. Google ScholarDigital Library
- Camil Demetrescu and Mikkel Thorup. Oracles for distances avoiding a link-failure. In 13th Symp. on Discrete Algorithms (SODA), 838--843. ACM-SIAM, 2002. Google ScholarDigital Library
- Pierre Fraigniaud, Emmanuelle Lebhar, and Laurent Viennot. The inframetric model for the internet. In 27th IEEE Conf. on Computer Communications (INFOCOM), 1085--1093, 2008.Google ScholarCross Ref
- Anupam Gupta, Robert Krauthgamer, and James R. Lee. Bounded geometries, fractals, and low-distortion embeddings. In 44th IEEE Symp. on Foundations of Computer Science (FOCS), 534--543, IEEE, 2003. Google ScholarDigital Library
- Cyril Gavoille and David Peleg. Compact and localized distributed data structures. Distributed Computing, 16(2-3):111--120, 2003. Google ScholarDigital Library
- Cyril Gavoille, David Peleg, Stéphane Pérennès, and Ran Raz. Distance labeling in graphs. J. Algorithms, 53(1):85--112, 2004. Google ScholarDigital Library
- Neelesh Khanna and Surender Baswana. Approximate shortest path oracle under vertex failure. In 26th Symp. on Theoretical Aspects of Computer Science (STACS), 2010.Google Scholar
- Dmitri Krioukov, KC Claffy, Kevin Fall, and Arthur Brady. On compact routing for the internet. ACM SIGCOMM Computer Communication Review, 37(3):43--52, 2007. Google ScholarDigital Library
- Dmitri Krioukov, Kevin Fall, and Xiaowei Yang. Compact routing on internet-like graphs. In 23rd Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM), volume 1, --219, 2004.Google ScholarCross Ref
- Goran Konjevod, Andréa Werneck Richa, and Donglin Xia. Optimal scale-free compact routing schemes in doubling networks. In 18th Symp. on Discrete Algorithms (SODA), 939--948. ACM-SIAM, 2007. Google ScholarDigital Library
- Goran Konjevod, Andréa Werneck Richa, and Donglin Xia. Dynamic routing and location services in metrics of low doubling dimension. In 22nd Int. Symp. on Distributed Computing (DISC), LNCS 5218, 379--393. SV, 2008. Google ScholarDigital Library
- David Peleg. Proximity-preserving labeling schemes and their applications. In Proc. 25th Workshop on Graph- Theoretic Concepts in Computer Science, 30--41, 1999. Google ScholarDigital Library
- C. Greg Plaxton, Rajmohan Rajaraman, and Andréa Werneck Richa. Accessing nearby copies of replicated objects in a distributed environment. In 9th ACM Symp. on Parallel Algorithms and Architectures (SPAA), 311--320, 1997. Google ScholarDigital Library
- Mihai Pǎtraşcu and Mikkel Thorup. Planning for fast connectivity updates. In 48th IEEE Symp. on Foundations of Computer Science (FOCS), 263--271, IEEE, 2007. Google ScholarDigital Library
- Aleksandrs Slivkins. Distance estimation and object location via rings of neighbors. In 24th ACM Symp. on Principles of Distributed Computing (PODC), 41--50, 2005. Google ScholarDigital Library
- Aleksandrs Slivkins. Distance estimation and object location via rings of neighbors. Distributed Computing, 19(4):313--333, 2007.Google ScholarDigital Library
- Kunal Talwar. Bypassing the embedding: Algorithms for low dimensional metrics. In 36th ACM Symp. on Theory of Computing (STOC), 281--290, 2004. Google ScholarDigital Library
- Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. J. ACM, 51(6):993--1024, 2004. Google ScholarDigital Library
- David Andrew Twigg. Forbidden-set Routing. PhD thesis, University of Cambridge (King's College), 2006.Google Scholar
Index Terms
- Forbidden-set distance labels for graphs of bounded doubling dimension
Recommendations
Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computingThis paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels ...
Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension
This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O(1 + ϵ− ...
Forbidden Subgraphs and Weak Locally Connected Graphs
A graph is called H-free if it has no induced subgraph isomorphic to H. A graph is called $$N^i$$Ni-locally connected if $$G[\{ x\in V(G): 1\le d_G(w, x)\le i\}]$$G[{x?V(G):1≤dG(w,x)≤i}] is connected and $$N_2$$N2-locally connected if $$G[\{uv: \{uw, vw\...
Comments