We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Computer architecture is about to undergo, if not another revolution, then a vigorous shaking-up. The major chip manufacturers have, for the time being, simply given up trying to make processors run faster. Instead, they have recently started shipping "multicore" architectures, in which multiple processors (cores) communicate directly through shared hardware caches, providing increased concurrency instead of increased clock speed.As a result, system designers and software engineers can no longer rely on increasing clock speed to hide software bloat. Instead, they must somehow learn to make effective use of increasing parallelism. This adaptation will not be easy. Conventional synchronization techniques based on locks and conditions are unlikely to be effective in such a demanding environment. Coarse-grained locks, which protect relatively large amounts of data, do not scale, and fine-grained locks introduce substantial software engineering problem.Transactional memory is a computational model in which threads synchronize by optimistic, lock-free transactions. This synchronization model promises to alleviate many (not all) of the problems associated with locking, and there is a growing community of researchers working on both software and hardware support for this approach. This talk will survey the area, with a focus on open research problems.

The Art of Multiprocessor Programming

Network traffic measurements provide essential data for networking research and network management. In this article we describe a passive monitoring system designed to capture GPS synchronized packet-level traffic measurements on OC-3, OC-12, and OC-48 links. Our system is deployed in four POP in the Sprint IP backbone. Measurement data is stored on a 10 Tbyte storage area network and analyzed on a computing cluster. We present a set of results to both demonstrate the strength of the system and identify recent changes in Internet traffic characteristics. The results include traffic workload, analyses of TCP flow round-trip times, out-of-sequence packet rates, and packet delay. We also show that some links no longer carry Web traffic as their dominant component to the benefit of file sharing and media streaming. On most links we monitored, TCP flows exhibit low out-of-sequence packet rates, and backbone delays are dominated by the speed of light.

/pdf/packet-level-traffic-measurements-from-the-sprint-ip-7esl6ncnyi.pdf

Packet-level traffic measurements from the Sprint IP backbone

Stephen J. Hartley Oxford University Press, New York, 1998, 260 pp. ISBN 0-19-511315-2, $45.00 Concurrent Programming  is a thorough treatment of Java multi-threaded programming for both a stand-alone and distributed environment. Designed mostly for students in concurrent or parallel programming classes, the text is also an excellent reference for the practicing professional developing multi-threaded programs or applets. Hartley first provides a complete explanation of the features of Java necessary to write concurrent programs, including topics such as exception handling, interfaces, and packages. He then gives the reader a solid background to write multi-threaded programs and also presents the problems introduced when writing concurrent programs—namely race conditions, mutual exclusion, and deadlock. Hartley also provides several software solutions that do not require the use of common process and thread mechanisms. Once the groundwork is laid for writing concurrent programs, Hartley then takes a different approach than most Java references. Rather than presenting how Java handles mutual exclusion with the  synchronized  keyword (although it is covered later), he first looks at semaphore-based solutions to classic concurrent problems such as bounded-buffer, readers-writers, and the dining philosophers. Hartley also uses the same approach to develop Java classes for monitors and message passing. This unique approach to introducing concurrency allows the readers to both understand how Java threads are synchronized and how the basic synchronization mechanism can be used to construct more abstract tools such as semaphores. If there is a shortcoming with the text it is with the lack of sufficient coverage of remote method invocation (RMI), although there is a section covering RMI. This is quite understandable as RMI is a fairly recent phenomenon with the Java community. Also, the classes that Hartley provides could easily implement RMI rather than sockets to handle communication. The strengths of the book include its ease in reading, several examples at the end of chapters, a package similar to Xtango that provides algorithm animation, and a supportive web site by the author (see  www.mcs.drexel.edu/~shartley/ConcProgJava/index.html ) including compressed source code. As Java becomes more dominant on the server side of multi-tier applications, writing thread-safe concurrent applications becomes even more important.  Concurrent Programming  is a strong step towards teaching students and professionals such skills. Greg Gagne, Westminster College of Salt Lake City Salt Lake City, Utah

Distributed Computing: Fundamentals, Simulations and Advanced Topics

Buffers in on-chip networks consume significant energy, occupy chip area, and increase design complexity. In this paper, we make a case for a new approach to designing on-chip interconnection networks that eliminates the need for buffers for routing or flow control. We describe new algorithms for routing without using buffers in router input/output ports. We analyze the advantages and disadvantages of bufferless routing and discuss how router latency can be reduced by taking advantage of the fact that input/output buffers do not exist. Our evaluations show that routing without buffers significantly reduces the energy consumption of the on-chip cache/processor-to-cache network, while providing similar performance to that of existing buffered routing algorithms at low network utilization (i.e., on most real applications). We conclude that bufferless routing can be an attractive and energy-efficient design option for on-chip cache/processor-to-cache networks where network utilization is low.

/pdf/a-case-for-bufferless-routing-in-on-chip-networks-2e289wpkbm.pdf

A case for bufferless routing in on-chip networks

A classic optimization problem in network routing is to minimize C + D, where C is the maximum edge congestion and D is the maximum path length (also known as dilation). The problem of computing the optimal C* + D* is NP-complete even when either C* or D* is a small constant. We study routing games in general networks where each player i selfishly selects a path that minimizes Ci + Di the sum of congestion and dilation of the player's path. We first show that there are instances of this game without Nash equilibria. We then turn to the related quality of routing (QoR) games which always have Nash equilibria. QoR games represent networks with a small number of service classes where paths in different classes do not interfere with each other (with frequency or time division multiplexing). QoR games have O(log4 n) price of anarchy when either C* or D* is a constant. Thus, Nash equilibria of QoR games give poly-log approximations to hard optimization problems.

https://www.cct.lsu.edu/~xuelin/routing/Approximating%20Congestion%20+%20Dilation%20in%20Networks.pdf

Approximating Congestion + Dilation in Networks via "Quality of Routing&#x201D; Games

A MAC protocol specifies how nodes in a sensor network access a shared communication channel. Desired properties of such MAC protocol are: it should be distributed and contention-free (avoid collisions); it should self-stabilize to changes in the network (such as arrival of new nodes), and these changes should be contained, i.e., affect only the nodes in the vicinity of the change; it should not assume that nodes have a global time reference, i.e., nodes may not be time-synchronized. We give the first MAC protocols that satisfy all of these requirements, i.e., we give distributed, contention-free, self-stabilizing MAC protocols which do not assume a global time reference. Our protocols self-stabilize from an arbitrary initial state, and if the network changes the changes are contained and the protocol adjusts to the local topology of the network. The communication complexity, number and size of messages, for the protocol to stabilize is small (logarithmic in network size).

/pdf/contention-free-mac-protocols-for-wireless-sensor-networks-rb64jh396a.pdf

Contention-free MAC protocols for wireless sensor networks

Link reversal algorithms provide a simple mechanism for routing in mobile ad hoc networks. These algorithms maintain routes to any particular destination in the network, even when the network topology changes frequently. In link reversal, a node reverses its incident links whenever it loses routes to the destination. Link reversal algorithms have been studied experimentally and have been used in practical routing algorithms, including [8].This paper presents the first formal performance analysis of link reversal algorithms. We study these algorithms in terms of work (number of node reversals) and the time needed until the network stabilizes to a state in which all the routes are reestablished. We focus on the full reversal algorithm and the partial reversal algorithm, both due to Gafni and Berstekas [5]; the first algorithm is simpler, while the latter has been found to be more efficient for typical cases. Our results are as follows:(1) The full reversal algorithm requires O(n2) work and time, where n is the number of nodes which have lost the routes to the destination.(2) The partial reversal algorithm requires O(n • a* + n2) work and time, where a* is a non-negative integer which depends on the state of the network. This bound is tight in the worst case, for any a*.(3) There are networks such that for every deterministic link reversal algorithm, there are initial states which require requires ω(n2) work and time to stabilize. Therefore, surprisingly, the full reversal algorithm is asymptotically optimal in the worst case, while the partial reversal algorithm is not, since a* can grow arbitrarily large.

http://theory.csail.mit.edu/classes/6.885/spring06/papers/BuschST.pdf

Analysis of link reversal routing algorithms for mobile ad hoc networks

Atomic routing games on maximum congestion

We study the problem of maintaining sketches of recent elements of a data stream. Motivated by applications involving network data, we consider streams that are asynchronous, in which the observed order of data is not the same as the time order in which the data was generated. The notion of recent elements of a stream is modeled by the sliding timestamp window, which is the set of elements with timestamps that are close to the current time. We design algorithms for maintaining sketches of all elements within the sliding timestamp window that can give provably accurate estimates of two basic aggregates, the sum and the median, of a stream of numbers. The space taken by the sketches, the time needed for querying the sketch, and the time for inserting new elements into the sketch are all polylog with respect to the maximum window size and the values of the data items in the window. Our sketches can be easily combined in a lossless and compact way, making them useful for distributed computations over data streams. Previous works on sketching recent elements of a data stream have all considered the more restrictive scenario of synchronous streams, where the observed order of data is the same as the time order in which the data was generated. Our notion of recency of elements is more general than that studied in previous work, and thus our sketches are more robust to network delays and asynchrony.

http://www.csc.lsu.edu/~busch/papers/conference/2006-PODC-streams.pdf

Costas Busch

Papers

Approximating Congestion + Dilation in Networks via "Quality of Routing” Games

Contention-free MAC protocols for wireless sensor networks

Analysis of link reversal routing algorithms for mobile ad hoc networks

Atomic routing games on maximum congestion

Sketching asynchronous streams over a sliding window

Costas Busch

Papers

Approximating Congestion + Dilation in Networks via "Quality of Routing&#x201D; Games

Contention-free MAC protocols for wireless sensor networks

Analysis of link reversal routing algorithms for mobile ad hoc networks

Atomic routing games on maximum congestion

Sketching asynchronous streams over a sliding window

Approximating Congestion + Dilation in Networks via "Quality of Routing” Games