Search

To find a maximum number of communication requests that can be satisfied concurrently, is a fundamental network scheduling problem. In this work we investigate the problem of finding a maximum number of multicast requests that can be scheduled simultaneously in a tree network in which the edges and links have heterogeneous bandwidth limitations.This problem generalizes two problems studied in the literature: maximum k-colorable subgraph in chordal graphs, maximum multi-commodity flow in trees. The problem is NP-hard and admits a 1.585-approximation in the special case of homogeneous bandwidth limitations.We first show that the problem is harder to approximate when the bandwidth limitations are heterogeneous, i.e. vary from link to link and from node to node. We then generalize of a classical algorithm and obtain an M-approximation where M is the maximum number of leaves of the communication subtrees. Surprisingly, variants of the same algorithm, are used in the literature at least four times to solve related problems. There exists a polynomial-time algorithm for the special case of unicast requests and star topology. We generalize this result and relax the second requirement so that the set of unicast requests share a common vertex with no restriction on the tree topology.

This study was carried in the context of the development of technologies for a cloud that uses an optical network for internal communication. The problem addressed in this paper deals with dispatching jobs - units of work, to be performed by machines on the cloud. Sending (or migrating) a job to a machine involves establishing a lightpath (a la circuit switching); this incurs a significant setup cost, but while it exists, the lightpath's capacity is very high. Hence, moving one job is about as expensive as moving a set of jobs over the same lightpath. Our goal is to develop online network dispatching algorithms for a work conserving job scheduling. That is, consider a set of jobs the dispatcher is responsible for their executions on some set $S_{M}$ of machines. Any machine in the network may join or (when not executing a job) leave $S_{M}$ according to decisions made outside the scope of this paper. Whenever a machine joins the set or is in the set and has just finished executing a job, it issues a request for a new job to perform and the dispatcher must send this machine a job that has not been executed yet (if such exists). Every machine can perform any of the jobs, and each job is performed on a single machine. The main algorithmic challenge in this context boils down to the following questions: How many jobs should we send to a requesting machine (or to some intermediate storage to be distributed from there)? From the storage on which machine should these jobs be taken? The algorithms developed here are shown to be efficient in reducing the costs of establishing lightpaths. As opposed to related algorithms for delivering consumable resources (in other contexts), we prove that our online algorithms are fully competitive. We present randomized online algorithms for two different settings: in the first it is assumed that each message requires establishing a lightpath and thus, incurs a setup cost; in the second, we distinguish between messages that carry job sets and small control messages sent by the algorithm, where the latter type of messages is assumed to be sent over a designated (non-optical) control plane at a negligible cost. Our algorithms are quite simple, though the analysis turns out to be rather involved. They are designed (and rigorously analyzed) for a general architecture, but would be especially efficient in fat tree architectures - the common choice in many data centers.

The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. We consider two problems in this model: (Δ+l)-vertex coloring and maximal independent set (MIS), for a network of unknown size $n$ and unknown maximum degree Δ. Solving these problems allows to overcome communication interferences, and to break symmetry, a core component of many distributed protocols. The presented results apply to general graphs, but are efficient in graphs with low edge density (sparse graphs), such as bounded degree graphs, planar graphs and graphs of bounded arboricity. We present O(Δ2 log n + Δ3) time deterministic uniform MIS and coloring protocols, which are asymptotically time optimal for bounded degree graphs. Furthermore, we devise O(a2 log2 n+a3log n) time MIS and coloring protocols, as well as O(a2 Δ 2 log2 n + a3 Δ 3 log n) time 2-hop MIS and 2-hop coloring protocols, where $a$ is the arboricity of the communication graph. Building upon the 2-hop coloring protocols, we show how the strong CONGEST model can be simulated and by using this simulation we obtain an O ( $a$ ) -coloring protocol. No results about coloring with less than Δ + 1 colors were known up to now in the beeping model.

The paper considers the design of energy-efficient online protocols for the basic problem of message transmission to hosts positioned at unknown distances in ad-hoc wireless networks. The paper formulates a number of variants of this problem and presents optimally competitive algorithms for those variants.

This paper considers the question of identifying the parameters governing the behavior of fundamental global network problems. Many papers on distributed network algorithms consider the task of optimizing the running time successful when an O(n) bound is achieved on an n-vertex network. We propose that a more sensitive parameter is the network's diameter Diam. This is demonstrated in the paper by providing a distributed minimum-weight spanning tree algorithm whose time complexity is sub-linear in n, but linear in Diam (specifically, O(Diam+n/sup 0.614/)). Our result is achieved through the application of graph decomposition and edge elimination techniques that may be of independent interest. >

We focus on wavelength allocation schemes for all-optical WDM ring networks. For an N node network we characterize the traffic by its load L/sub max/ (the maximum number of lightpaths that share a link) and do not assume knowledge of the arrival/departure processes. We prove that shortest path routing produces a routing which has at most twice the load of the optimal solution. We show that at least 0.5 L/sub max/ log/sub 2/N+L/sub max/ wavelengths are required by any algorithm in the worst case, and develop an algorithm which requires up to 3 L/sub max/ log/sub 2/N wavelengths. For the case when the load is high and blocking is necessary we present an improved algorithm.

The delivery of large files to single users, such as application programs for some versions of the envisioned network computer, or movies, is expected by many to be one of the main requirements of communication networks. This requires expensive high bandwidth capacity as well as fast and high storage servers. This motivates multimedia providers to optimize the delivery distances, as well as the electronic content allocation. A hierarchical architecture for providing the multimedia content was introduced by Nussbaumer, Patel, Schaffa, and Sternbenz (1994). They also introduced the trade-off between bandwidth and storage requirements for the placement of the content servers on the hierarchy tree. They found the best level of the hierarchy for the server location to minimize the total of the costs of communication and storage. Their algorithm is centralized. We solve the more general ease where servers can be located at different levels of the hierarchy. Our algorithm is distributed, and each node requires a limited memory capacity and computational power. Results for related approaches to caching design are of higher complexity. Results for related classic operations research problems are for centralized algorithms, mostly linear programming, that are not easy to convert into distributed algorithms. Instead, we observe that the use of dynamic programming is more natural for distributed implementations. For the specific problem at hand, we also managed to find a natural function (a generalization of the problem) that simplifies the combination operation used in dynamic programming. We also show how to map such contemporary problems to the area of classical plant location problems in operations research.

This article deals with store-and-forward deadlock prevention in communication networks. The approach we adopt is that of establishing buffer classes in order to prevent cyclic waiting chains. This type of solutions usually tends to require many buffers. The main contribution is in showing that the number of required buffers can be reduced considerably by employing a hierarchical organization of the network. It proposes a new hierarchical scheme for arbitrary networks, that features a tradeoff between the communication overhead and the buffer requirements of the routing. This tradeoff can be shown to be close to optimal. >