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45
Coloring unstructured radio networks
, 2005
"... During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as ..."
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Cited by 36 (9 self)
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During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as a foundation for more sophisticated algorithms. In this paper, we consider the problem of obtaining a vertex coloring as such an initial structure. We propose an algorithm that works in the unstructured radio network model. This model captures the characteristics of newly deployed ad hoc and sensor networks, i.e. asynchronous wakeup, no collisiondetection, and scarce knowledge about the network topology. When modeling the network as a graph with bounded independence, our algorithm produces a correct coloring with O(∆) colors in time O( ∆ log n) with high probability, where n and ∆ are the number of nodes in the network and the maximum degree, respectively. Also, the number of locally used colors depends only on the local node density. Graphs with bounded independence generalize unit disk graphs as well as many other wellknown models for
Optimal Clock Synchronization in Networks
"... Having access to an accurate time is a vital building block in all networks; in wireless sensor networks even more so, because wireless media access or data fusion may depend on it. Starting out with a novel analysis, we show that orthodox clock synchronization algorithms make fundamental mistakes. ..."
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Cited by 22 (7 self)
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Having access to an accurate time is a vital building block in all networks; in wireless sensor networks even more so, because wireless media access or data fusion may depend on it. Starting out with a novel analysis, we show that orthodox clock synchronization algorithms make fundamental mistakes. The stateoftheart clock synchronization algorithm FTSP exhibits an error that grows exponentially with the size of the network, for instance. Since the involved parameters are small, the error only becomes visible in midsize networks of about 1020 nodes. In contrast, we present PulseSync, a new clock synchronization algorithm that is asymptotically optimal. We evaluate PulseSync on a Mica2 testbed, and by simulation on larger networks. On a 20 node network, the prototype implementation of PulseSync outperforms FTSP by a factor of 5. Theory and simulation show that for larger networks, PulseSync offers an accuracy which is several orders of magnitude better than FTSP. To round off the presentation, we investigate several optimization issues, e.g. media access and local skew.
A New Technique For Distributed Symmetry Breaking
 In Symp. on Principles of Distributed Computing
, 2010
"... We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tra ..."
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Cited by 19 (6 self)
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We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tradeoff. To get a ∆ + 1 coloring takes time O(log ∆ + √ log n). To obtain an O( ∆ + log 1+1 / log ∗ n n) coloring takes time O(log ∗ n). This is more than an exponential improvement in time for graphs of polylogarithmic degree. Our fastest algorithm works in constant time using O( ∆ log (c) n + log 1+1/c n) colors, where c denotes an arbitrary constant and log (c) n denotes the c times (recursively) applied logarithm to n. We also use the MultiTrials technique to compute network decompositions and to compute maximal independent set (MIS), obtaining new results for several graph classes.
Leveraging Linial’s Locality Limit
"... www.dcg.ethz.ch Abstract. In this paper we extend the lower bound technique by Linial for local coloring and maximal independent sets. We show that constant approximations to maximum independent sets on a ring require at least logstar time. More generally, the product of approximation quality and r ..."
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Cited by 17 (8 self)
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www.dcg.ethz.ch Abstract. In this paper we extend the lower bound technique by Linial for local coloring and maximal independent sets. We show that constant approximations to maximum independent sets on a ring require at least logstar time. More generally, the product of approximation quality and running time cannot be less than logstar. Using a generalized ring topology, we gain identical lower bounds for approximations to minimum dominating sets. Since our generalized ring topology is contained in a number of geometric graphs such as the unit disk graph, our bounds directly apply as lower bounds for quite a few algorithmic problems in wireless networking. Having in mind these and other results about local approximations of maximum independent sets and minimum dominating sets, one might think that the former are always at least as difficult to obtain as the latter. Conversely, we show that graphs exist, where a maximum independent set can be determined without any communication, while finding even an approximation to a minimum dominating set is as hard as in general graphs. 1
Sublogarithmic Distributed MIS Algorithm for Sparse Graphs using NashWilliams Decomposition
 In Journal of Distributed Computing Special Issue of selected papers from PODC
, 2008
"... We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on gr ..."
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Cited by 15 (2 self)
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We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graphtheoretic structure, called NashWilliams forestsdecomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearlytight lower bounds on the running time of any distributed algorithm for computing a forestsdecomposition.
Bounds On Contention Management Algorithms
"... We present two new algorithms for contention management in transactional memory, the deterministic algorithm CommitRounds and the randomized algorithm RandomizedRounds. Our randomized algorithm is efficient: in some notorious problem instances (e.g., dining philosophers) it is exponentially faster t ..."
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Cited by 12 (6 self)
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We present two new algorithms for contention management in transactional memory, the deterministic algorithm CommitRounds and the randomized algorithm RandomizedRounds. Our randomized algorithm is efficient: in some notorious problem instances (e.g., dining philosophers) it is exponentially faster than prior work from a worst case perspective. Both algorithms are (i) local and (ii) starvationfree. Our algorithms are local because they do not use global synchronization data structures (e.g., a shared counter), hence they do not introduce additional resource conflicts which eventually might limit scalability. Our algorithms are starvationfree because each transaction is guaranteed to complete. Prior work sometimes features either (i) or (ii), but not both. To analyze our algorithms (from a worst case perspective) we introduce a new measure of complexity that depends on the number of actual conflicts only. In addition, we show that even a nonconstant approximation of the length of an optimal (shortest) schedule of a set of transactions is NPhard – even if all transactions are known in advance and do not alter their resource requirements. Furthermore, in case the needed resources of a transaction varies over time, such that for a transaction the number of conflicting transactions increases by a factor k, the competitive ratio of any contention manager is Ω(k) for k < √ m, where m denotes the number of cores. 1
Coloring Unstructured Wireless MultiHop Networks
 In PODC
, 2009
"... We present a randomized coloring algorithm for the unstructured radio network model, a model comprising autonomous nodes, asynchronous wakeup, no collision detection and an unknown but geometric network topology. The current stateoftheart coloring algorithm needs with high probability O(∆·log n) ..."
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Cited by 10 (5 self)
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We present a randomized coloring algorithm for the unstructured radio network model, a model comprising autonomous nodes, asynchronous wakeup, no collision detection and an unknown but geometric network topology. The current stateoftheart coloring algorithm needs with high probability O(∆·log n) time and uses O(∆) colors, where n and ∆ are the number of nodes in the network and the maximum degree, respectively; this algorithm requires knowledge of a linear bound on n and ∆. We improve this result in three ways: Firstly, we improve the time complexity, instead of the logarithmic factor we just need a polylogarithmic additive term; more specifically, our time complexity is O( ∆ + log ∆ · log n) given an estimate of n and ∆, and O( ∆ + log 2 n) without knowledge of ∆. Secondly, our vertex coloring algorithm needs ∆ + 1 colors only. Thirdly, our algorithm manages to do a distanced coloring with asymptotically optimal O(∆) colors for a constant d.
Distributed (∆ + 1)coloring in linear (in ∆) time
 In Proc. 41st Annual ACM Symposium on Theory of Computing (STOC
, 2009
"... The distributed ( ∆ + 1)coloring problem is one of most fundamental and wellstudied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current stateoftheart running time is O( ∆ log ∆+log ∗ ..."
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Cited by 10 (0 self)
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The distributed ( ∆ + 1)coloring problem is one of most fundamental and wellstudied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current stateoftheart running time is O( ∆ log ∆+log ∗ n), due to Kuhn and Wattenhofer, PODC’06. Linial (FOCS’87) has proved a lower bound of 1 2 log ∗ n for the problem, and Szegedy and Vishwanathan (STOC’93) provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve running time smaller than Θ( ∆ log ∆). We present a deterministic (∆+1)coloring distributed algorithm with running time O(∆)+ 1
Deploying Wireless Networks with Beeps
"... We present the discrete beeping communication model, which assumes nodes have minimal knowledge about their environment and severely limited communication capabilities. Specifically, nodes have no information regarding the local or global structure of the network, do not have access to synchronized ..."
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Cited by 10 (2 self)
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We present the discrete beeping communication model, which assumes nodes have minimal knowledge about their environment and severely limited communication capabilities. Specifically, nodes have no information regarding the local or global structure of the network, do not have access to synchronized clocks and are woken up by an adversary. Moreover, instead on communicating through messages they rely solely on carrier sensing to exchange information. This model is interesting from a practical point of view, because it is possible to implement it (or emulate it) even in extremely restricted radio network environments. From a theory point of view, it shows that complex problems (such as vertex coloring) can be solved efficiently even without strong assumptions on properties of the communication model. We study the problem of interval coloring, a variant of vertex coloring specially suited for the studied beeping model. Given a set of resources, the goal of interval coloring is to assign every node a large contiguous fraction of the resources, such that neighboring nodes have disjoint resources. A kinterval coloring is one where every node gets at least a 1/k fraction of the resources. To highlight the importance of the discreteness of the model, we contrast it against a continuous variant described in [17]. We present an O(1) time algorithm that with probability 1 produces a O(∆)interval coloring. This improves an O(log n) time algorithm with the same guarantees presented in [17], and accentuates the unrealistic assumptions of the continuous model. Under the more realistic discrete model, we present a Las Vegas algorithm that solves O(∆)interval coloring in O(log n) time with high probability and describe how to adapt the algorithm for dynamic networks where nodes may join or leave. For constant degree graphs we prove a lower bound of Ω(log n) on the time required to solve interval coloring for this model against randomized algorithms. This lower bound implies that our algorithm is asymptotically optimal for constant degree graphs.
What can be approximated locally?  Case study: dominating sets in planar graphs
 SPAA'08
, 2008
"... Whether local algorithms can compute constant approximations of NPhard problems is of both practical and theoretical interest. So far, no algorithms achieving this goal are known, as either the approximation ratio or the running time exceed O(1), or the nodes are provided with nontrivial additiona ..."
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Cited by 9 (1 self)
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Whether local algorithms can compute constant approximations of NPhard problems is of both practical and theoretical interest. So far, no algorithms achieving this goal are known, as either the approximation ratio or the running time exceed O(1), or the nodes are provided with nontrivial additional information. In this paper, we present the first distributed algorithm approximating a minimum dominating set on a planar graph within a constant factor in constant time. Moreover, the nodes do not need any additional information.