Reuven Bar-Yehuda

On the time-complexity of broadcast in multi-hop radio networks: an exponential gap between determinism and randomization

The time-complexity of deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multi-hop radio networks is investigated. In many such networks, communication takes place in synchronous time-slots. A processor receives a message at a certain time-slot if exactly one of its neighbors transmits at that time-slot. We assume no collision-detection mechanism; i.e., it is not always possible to distinguish the case where no neighbor transmits from the case where several neighbors transmit simultaneously. We present a randomized protocol that achieves broadcast in time which is optimal up to a logarithmic factor. In particular, with probability 1 --E, the protocol achieves broadcast within O((D + log n/s) ‘log n) time-slots, where n is the number of processors in the network and D its diameter. On the other hand, we prove a linear lower bound on the deterministic time-complexity of broadcast in this model. Namely, we show that any deterministic broadcast protocol requires 8(n) time-slots, even if the network has diameter 3, and n is known to all processors. These two results demonstrate an exponential gap in complexity between randomization and determinism.

A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem

A local-ratio theorem for approximating the weighted vertex cover problem is presented. It consists of reducing the weights of vertices in certain subgraphs and has the effect of local-approximation. Putting together the Nemhauser-Trotter local optimization algorithm and the local-ratio theorem yields several new approximation techniques which improve known results from time complexity, simplicity and performance-ratio point of view. The main approximation algorithm guarantees a ratio of where K is the smallest integer s.t. † This is an improvement over the currently known ratios, especially for a “practical” number of vertices (e.g. for graphs which have less than 2400, 60000, 10 12 vertices the ratio is bounded by 1.75, 1.8, 1.9 respectively).

A unified approach to approximating resource allocation and scheduling

We present a general framework for solving resource allocation and scheduling problems. Given a resource of fixed size, we present algorithms that approximate the maximum throughput or the minimum loss by a constant factor. Our approximation factors apply to many problems, among which are: (i) real-time scheduling of jobs on parallel machines, (ii) bandwidth allocation for sessions between two endpoints, (iii) general caching, (iv) dynamic storage allocation, and (v) bandwidth allocation on optical line and ring topologies. For some of these problems we provide the first constant factor approximation algorithm. Our algorithms are simple and efficient and are based on the local-ratio technique. We note that they can equivalently be interpreted within the primal-dual schema.

A linear-time approximation algorithm for the weighted vertex cover problem

Abstract A linear time approximation algorithm for the weighted set-covering problem is presented. For the special case of the weighted vertex cover problem it produces a solution of weight which is at most twice the weight of an optimal solution.

On the time-complexity of broadcast in radio networks: an exponential gap between determinism randomization

The time-complexity of deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multi-hop radio networks is investigated. In many such networks, communication takes place in synchronous time-slots. A processor receives a message at a certain time-slot if exactly one of its neighbors transmits at that time-slot. We assume no collision-detection mechanism; i.e., it is not always possible to distinguish the case where no neighbor transmits from the case where several neighbors transmit simultaneously. We present a randomized protocol that achieves broadcast in time which is optimal up to a logarithmic factor. In particular, with probability 1 --E, the protocol achieves broadcast within O((D + log n/s) ‘log n) time-slots, where n is the number of processors in the network and D its diameter. On the other hand, we prove a linear lower bound on the deterministic time-complexity of broadcast in this model. Namely, we show that any deterministic broadcast protocol requires 8(n) time-slots, even if the network has diameter 3, and n is known to all processors. These two results demonstrate an exponential gap in complexity between randomization and determinism. l i ‘ 1992 Academic press, IX

Multiple communication im multihop radio networks

Two tasks of communication in a multihop synchronous radio network are considered: Point-to-point communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowledge messages deterministically.Let n, D, and

Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference

\Delta

Randomized algorithms for the loop cutset problem

be the number of nodes, the diameter and the maximum degree of our network, respectively. Both protocols require a setup phase in which a BFS tree is constructed. This phase takes

Efficient emulation of single-hop radio network with collision detection on multi-hop radio network with no collision detection

O((n + D\log n)\log \Delta )

Multiple communication in multi-hop radio networks

time.After the setup, k point-to-point transmissions require