Minimizing Flow Time in the Wireless Gathering Problem

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than \Omega(m^{1/3) when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to

A generalized parallel task model for recurrent real-time processes

A model is considered for representing recurrent precedence-constrained tasks that are to execute on multiprocessor platforms. A recurrent task is specified as a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and need to complete execution within the specified relative deadline of their release. Each task may release j

On the Efficiency of Restricted Tolls in Non-atomic Network Routing Games

An effective means to reduce the inefficiency of Nash flows in non- atomic network routing games is to impose tolls on the arcs of the network. It is a well-known fact that marginal cost tolls induce a Nash flow that corresponds to a minimum cost flow. However, despite their effectiveness, marginal cost tolls suffer from two major drawbacks, namely (i) that potentially every arc of the network is tolled, and (ii) that the imposed tolls can be arbitrarily large. In this paper, we study the restricted network toll problem in which tolls can be imposed on the arcs of the network but are restricted to not exceed a predefined threshold for every arc. We show that optimal restricted tolls can be computed efficiently for parallel-arc networks and affine latency functions. This generalizes a previous work on taxing subnetworks to arbitrary restrictions. Our algorithm is quite simple, but relies on solving several convex programs. The key to our approach is a characterization of the flows that are inducible by restricted tolls for single-commodity networks. We also derive bounds on the efficiency of restricted tolls for multi-commodity networks and polynomial latency functions. These bounds are tight even for parallel-arc networks. Our bounds show that restricted tolls can significantly reduce the price of anarchy if the restrictions imposed on arcs with high-degree polynomials are not too severe. Our proof is constructive. We define tolls respecting the given thresholds and show that these tolls lead to a reduced price of anarchy by using a (\lambda,\mu)-smoothness approach

An approximation algorithm for the Wireless Gathering Problem

The Wireless Gathering Problem is to find an interference-free schedule for data gathering in a wireless network in minimum time. We present a 4-approximate polynomial-time on-line algorithm for this NP-hard problem. We show that no shortest path following algorithm can have an approximation ratio better than 4

The Distributed Wireless Gathering Problem

We address the problem of data gathering in a wireless network using multihop communication; our main goal is the analysis of simple algorithms suitable for implementation in realistic scenarios. We study the performance of distributed algorithms, which do not use any form of local coordination, and we focus on the objective of minimizing average flow times of data packets. We prove a lower bound of Ω(logm) on the competitive ratio of any distributed algorithm minimizing the maximum flow time, where m is the number of packets. Next, we consider a distributed algorithm which sends packets over shortest paths, and we use resource augmentation to analyze its performance when the objective is to minimize the average flow time. If interferences are modeled as in Bar-Yehuda et al. (J. of Computer and Systems Science, 1992) we prove that the algorithm is (1 + ε)-competitive, when the algorithm sends packets a factor O(log(δ/ε) logΔ) faster than the optimal offline solution; here δ is the diameter of the network and Δ the maximum degree. We finally extend this result to a more complex interference model