Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
Computing on an anonymous ring
Journal of the ACM (JACM)
Locality in distributed graph algorithms
SIAM Journal on Computing
SIAM Journal on Computing
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Leader Election Problem on Networks in which Processor Identity Numbers Are Not Distinct
IEEE Transactions on Parallel and Distributed Systems
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Local computations on static and dynamic graphs
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Constant-time distributed dominating set approximation
Distributed Computing
Fault-Tolerant Clustering in Ad Hoc and Sensor Networks
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
Fast Distributed Approximations in Planar Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Leveraging Linial's Locality Limit
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the girth of random Cayley graphs
Random Structures & Algorithms
Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
A local 2-approximation algorithm for the vertex cover problem
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Distributed algorithms for edge dominating sets
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
On the limitations of the use of solvable groups in Cayley graph cage constructions
European Journal of Combinatorics
Efficient distributed weighted matchings on trees
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Distributed maximal matching: greedy is optimal
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Lower bounds for local approximation
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Weak models of distributed computing, with connections to modal logic
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Deterministic local algorithms, unique identifiers, and fractional graph colouring
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
ACM Computing Surveys (CSUR)
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In the study of deterministic distributed algorithms, it is commonly assumed that each node has a unique O(log n)-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms) do not need such identifiers: a port numbering and orientation is sufficient. Our result holds for so-called simple PO-checkable graph optimisation problems; this includes many classical packing and covering problems such as vertex covers, edge covers, matchings, independent sets, dominating sets, and edge dominating sets. We focus on the case of bounded-degree graphs and show that if a local algorithm finds a constant-factor approximation of a simple PO-checkable graph problem with the help of unique identifiers, then the same approximation ratio can be achieved on anonymous networks. As a corollary of our result, we derive a tight lower bound on the local approximability of the minimum edge dominating set problem. By prior work, there is a deterministic local algorithm that achieves the approximation factor of 4--1/⌊Δ/2⌋ in graphs of maximum degree Δ. This approximation ratio is known to be optimal in the port-numbering model—our main theorem implies that it is optimal also in the standard model in which each node has a unique identifier. Our main technical tool is an algebraic construction of homogeneously ordered graphs: We say that a graph is (α,r)-homogeneous if its nodes are linearly ordered so that an α fraction of nodes have pairwise isomorphic radius-r neighbourhoods. We show that there exists a finite (α,r)-homogeneous 2k-regular graph of girth at least g for any α r, k, and g.