Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Maximizing the Lifetime of Dominating Sets
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 12 - Volume 13
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Energy conservation via domatic partitions
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
A fast localized algorithm for scheduling sensors
Journal of Parallel and Distributed Computing - Special issue: Algorithms for wireless and ad-hoc networks
An improved exact algorithm for the domatic number problem
Information Processing Letters
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Packing element-disjoint steiner trees
ACM Transactions on Algorithms (TALG)
Improved algorithmic versions of the Lovász Local Lemma
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Monitoring schedules for randomly deployed sensor networks
Proceedings of the fifth international workshop on Foundations of mobile computing
Approximate min--max theorems for Steiner rooted-orientations of graphs and hypergraphs
Journal of Combinatorial Theory Series B
Decomposition of multiple coverings into many parts
Computational Geometry: Theory and Applications
Distributed Generation of a Family of Connected Dominating Sets in Wireless Sensor Networks
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
Approximation Algorithms for Domatic Partitions of Unit Disk Graphs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Sleep scheduling for wireless sensor networks via network flow model
Computer Communications
Disjoint bases in a polymatroid
Random Structures & Algorithms
Local approximation algorithms for scheduling problems in sensor networks
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Energy efficient monitoring in sensor networks
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
Disjoint dominating and total dominating sets in graphs
Discrete Applied Mathematics
Cooperative caching and relaying strategies for peer-to-peer content delivery
IPTPS'08 Proceedings of the 7th international conference on Peer-to-peer systems
Hardness of k-Vertex-Connected Subgraph Augmentation Problem
Journal of Combinatorial Optimization
Using sticker model of DNA computing to solve domatic partition, kernel and induced path problems
Information Sciences: an International Journal
Tight Approximation Algorithms for Maximum Separable Assignment Problems
Mathematics of Operations Research
Complexity of total {k}-domination and related problems
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Optimal network locality in distributed virtualized data-centers
Computer Communications
Inapproximability results for combinatorial auctions with submodular utility functions
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Packing element-disjoint steiner trees
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
DCOSS'10 Proceedings of the 6th IEEE international conference on Distributed Computing in Sensor Systems
Buying Cheap Is Expensive: Approximability of Combinatorial Pricing Problems
SIAM Journal on Computing
Randomized algorithms and probabilistic analysis in wireless networking
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
The algorithmic complexity of k-domatic partition of graphs
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
ACM Computing Surveys (CSUR)
Domatic partition in homogeneous wireless sensor networks
Journal of Network and Computer Applications
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A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a graph into the maximum number of disjoint dominating sets. Let n denote the number of vertices, $\delta$ the minimum degree, and $\Delta$ the maximum degree.We show that every graph has a domatic partition with $(1 - o(1))(\delta + 1)/\ln n$ dominating sets and, moreover, that such a domatic partition can be found in polynomial-time. This implies a $(1 + o(1))\ln n$-approximation algorithm for domatic number, since the domatic number is always at most $\delta + 1$. We also show this to be essentially best possible. Namely, extending the approximation hardness of set cover by combining multiprover protocols with zero-knowledge techniques, we show that for every $\epsilon 0$, a $(1 - \epsilon)\ln n$-approximation implies that $NP \subseteq DTIME(n^{O(\log\log n)})$. This makes domatic number the first natural maximization problem (known to the authors) that is provably approximable to within polylogarithmic factors but no better.We also show that every graph has a domatic partition with $(1 - o(1))(\delta + 1)/\ln \Delta$ dominating sets, where the "o(1)" term goes to zero as $\Delta$ increases. This can be turned into an efficient algorithm that produces a domatic partition of $\Omega(\delta/\ln \Delta)$ sets.