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A Unified Framework and Algorithm for Channel Assignment
 in Wireless Networks”, Wireless Networks, Volume 5, Issue 2
, 1999
"... Channel assignment problems in the time, frequency and code domains have thus far been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framew ..."
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Cited by 114 (0 self)
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Channel assignment problems in the time, frequency and code domains have thus far been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framework identifies eleven atomic constraints underlying most current and potential assignment problems, and characterizes a problem as a combination of these constraints. Based on this framework, we present a unified algorithm for efficient (T/F/C)DMA channel assignments to network nodes or to internodal links in a (multihop) wireless network. The algorithm is parametrized to allow for tradeoffselectable use as three different variants called RAND, MNF, and PMNF. We provide comprehensive theoretical analysis characterizing the worstcase performance of our algorithm for several classes of problems. In particular, we show that the assignments produced by the PMNF variant are proportional to the thickness of the network. For most typical multihop networks, the thickness can be bounded by a small constant, and hence this represents a significant theoretical result. We also experimentally study the relative performance of the variants for one node and one link assignment problem. We observe that the PMNF variant performs the best, and that a large percentage of unidirectional links is detrimental to the performance in general. 1.
A parallel algorithmic version of the local lemma
, 1991
"... The Lovász Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for ..."
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Cited by 60 (10 self)
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The Lovász Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of loosing a little in the estimates. His method does not seem to be parallelizable. Here we modify his technique and achieve an algorithmic version that can be parallelized, thus obtaining deterministic NC 1 algorithms for several interesting algorithmic problems.
Secure communication in minimal connectivity models
 Journal of Cryptology
, 1998
"... Abstract. Problems of secure communication and computation have been studied extensively in network models. In this work, we ask what is possible in the informationtheoretic setting when the adversary is very strong (Byzantine) and the network connectivity is very low (minimum needed for crashtole ..."
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Cited by 49 (1 self)
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Abstract. Problems of secure communication and computation have been studied extensively in network models. In this work, we ask what is possible in the informationtheoretic setting when the adversary is very strong (Byzantine) and the network connectivity is very low (minimum needed for crashtolerance). For some natural models, our results imply a sizable gap between the connectivity required for perfect security and for probabilistic security. Our results also have implications to the commonly studied simple channel model and to general secure multiparty computation. 1
Consensus and collision detectors in wireless ad hoc networks
 In PODC
, 2005
"... Abstract In this study, we consider the faulttolerant consensus problem in wireless ad hoc networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop wireless networks, where all nodes are located within broadcast range of each oth ..."
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Cited by 42 (19 self)
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Abstract In this study, we consider the faulttolerant consensus problem in wireless ad hoc networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop wireless networks, where all nodes are located within broadcast range of each other. In a novel break from existing work, we introduce a highly unpredictable communication model in which each node may lose an arbitrary subset of the messages sent by its neighbors during each round. We argue that this model better matches behavior observed in empirical studies of these networks. To cope with this communication unreliability we augment nodes with receiverside collision detectors and present a new classification of these detectors in terms of accuracy and completeness. This classification is motivated by practical realities and allows us to determine, roughly speaking, how much collision detection capability is enough to solve the consensus problem efficiently in this setting. We consider ten different combinations of completeness and accuracy properties in total, determining for each whether consensus is solvable, and, if it is, a lower bound on the number of rounds required. Furthermore, we distinguish anonymous and nonanonymous protocolswhere "anonymous " implies that devices do not have unique identifiersdetermining what effect (if any) this extra information has on the complexity of the problem. In all relevant cases, we provide matching upper bounds. Our contention is that the introduction of (possibly weak) receiverside collision detection is an important approach to reliably solving problems in unreliable networks. Our results, derived in a realistic network model, provide important feedback to ad hoc network practitioners regarding what hardware (and lowlayer software) collision detection capability is sufficient to facilitate the construction of reliable and faulttolerant agreement protocols for use in realworld deployments.
A Unified Framework and Algorithm for (T/F/C)DMA Channel Assignment in Wireless Networks
 in IEEE INFOCOM
, 1997
"... Channel assignment problems in the time, frequency and code domains have hitherto been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framew ..."
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Cited by 36 (0 self)
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Channel assignment problems in the time, frequency and code domains have hitherto been studied separately. Exploiting the similarity of constraints that characterize assignments within and across these domains, we introduce the first unified framework for the study of assignment problems. Our framework identifies eleven atomic constraints underlying most current and potential assignment problems, and characterizes a problem as a combination of these constraints. Based on this framework, we present a unified algorithm for efficient (T/F/C)DMA channel assignments to network nodes or to internodal links in a (multihop) wireless network. The algorithm is parametrized to allow for use as three different variants  RAND, MNF, and PMNF. We provide comprehensive theoretical analysis characterizing the worstcase performance of our algorithm for several classes of problems. In particular, we show that the assignments produced by the PMNF variant are proportional to the thickness of the network...
Secure Hypergraphs: Privacy from Partial Broadcast
 In Proceedings of the TwentySeventh Annual ACM Symposium on the Theory of Computing
, 1995
"... A "partial broadcast channel" enables one processor to send the same messagesimultaneously and privately to a fixed subset of processors. Suppose that a collection of processors are connected by an arbitrary network of partial broadcast channels (a hypergraph). We initiate the study of necess ..."
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Cited by 31 (2 self)
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A "partial broadcast channel" enables one processor to send the same messagesimultaneously and privately to a fixed subset of processors. Suppose that a collection of processors are connected by an arbitrary network of partial broadcast channels (a hypergraph). We initiate the study of necessary and sufficient conditions, complexity bounds, and protocols for individual processors to exchange private messages across this network. Private message exchange, in turn, enables the realization of general secure computation primitives. The model (motivated by various environments such as multicast network architectures and group communication in distributed systems) is an intermediate setting between the private channels model and the full information model, both of which have been investigated extensively in the last few years. We assume an allpowerful adversary (i.e., the information theoretic notion of security), and our techniques are combinatorial. Both the possibility and the poly...
Efficient Broadcasting using Network Coding
, 2008
"... We consider the problem of broadcasting in an adhoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life an ..."
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Cited by 30 (3 self)
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We consider the problem of broadcasting in an adhoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life and thus network lifetime. We prove that applying ideas from network coding allows to realize significant benefits in terms of energy efficiency for the problem of broadcasting, and propose very simple algorithms that allow to realize these benefits in practice. In particular, our theoretical analysis shows that network coding improves performance by a constant factor in fixed networks. We calculate this factor exactly for some canonical configurations. We then show that in networks where the topology dynamically changes, for example due to mobility, and where operations are restricted to simple distributed algorithms, network coding can offer improvements of a factor of log n, where n is the number of nodes in the network. We use the insights gained from the theoretical analysis to propose lowcomplexity distributed algorithms for realistic wireless adhoc scenarios, discuss a number of practical considerations, and evaluate our algorithms through packet level simulation.
Coloring Nonuniform Hypergraphs: A New Algorithmic Approach to the General Lovász Local Lemma
"... The Lovász Local Lemma (LLL) is a sieve method to prove the existence of certain structures with certain prescribed properties. In most of its applications the LLL does not supply a polynomialtime algorithm for finding these structures. Beck was the first who gave a method of converting some of the ..."
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Cited by 13 (3 self)
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The Lovász Local Lemma (LLL) is a sieve method to prove the existence of certain structures with certain prescribed properties. In most of its applications the LLL does not supply a polynomialtime algorithm for finding these structures. Beck was the first who gave a method of converting some of these existence proofs into efficient algorithmic procedures, at the cost of loosing a little in the estimates. He applied his technique to the symmetric form of the LLL and, in particular, to the problem of 2coloring uniform hypergraphs. In this paper we investigate the general form of the LLL. Our main result is a randomized algorithm for 2coloring nonuniform hypergraphs that runs in expected linear time. Even for uniform hypergraphs, no algorithm with such a runtime bound was previously known, and no polynomialtime algorithm was known at all for the class of nonuniform hypergraphs we will consider in this paper. Our algorithm and its analysis provide a novel approach to the general LLL that may be of independent interest. We also show how to extend our result to the ccoloring problem.
The Abstract MAC Layer
, 2009
"... A diversity of possible communication assumptions complicates the study of algorithms and lower bounds for radio networks. We address this problem by defining an Abstract MAC Layer. This service provides reliable local broadcast communication, with timing guarantees stated in terms of a collection o ..."
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Cited by 13 (11 self)
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A diversity of possible communication assumptions complicates the study of algorithms and lower bounds for radio networks. We address this problem by defining an Abstract MAC Layer. This service provides reliable local broadcast communication, with timing guarantees stated in terms of a collection of abstract delay functions applied to the relevant contention. Algorithm designers can analyze their algorithms in terms of these functions, independently of specific channel behavior. Concrete implementations of the Abstract MAC Layer over basic radio network models generate concrete definitions for these delay functions, automatically adapting bounds proven for the abstract service to bounds for the specific radio network under consideration. To illustrate this approach, we use the Abstract MAC Layer to study the new problem of MultiMessage Broadcast, a generalization of standard singlemessage broadcast, in which any number of messages arrive at any processes at any times. We present and analyze two algorithms for MultiMessage Broadcast in static networks: a simple greedy algorithm and one that uses regional leaders. We indicate how these results can be extended to mobile networks.
The Wireless Synchronization Problem
, 2009
"... In this paper, we study the wireless synchronization problem which requires devices activated at different times on a congested singlehop radio network to synchronize their round numbering. We assume a collection of n synchronous devices with access to a shared band of the radio spectrum, divided i ..."
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Cited by 13 (4 self)
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In this paper, we study the wireless synchronization problem which requires devices activated at different times on a congested singlehop radio network to synchronize their round numbering. We assume a collection of n synchronous devices with access to a shared band of the radio spectrum, divided into F narrowband frequencies. We assume that the communication medium suffers from unpredictable, perhaps even malicious interference, which we model by an adversary that can disrupt up to t frequencies per round. Devices begin executing in different rounds and the exact number of participants is not known in advance. “ We first prove a lower bound, demonstrating that at least log Ω