Towards better algorithms for parallel backtracking

Many algorithms in operations research and artificial intelligence are based on depth first search in implicitly defined trees. For parallelizing these algorithms, a load balancing scheme is needed which is able to evenly distribute parts of an irregularly shaped tree over the processors. It should work with minimal interprocessor communication and without prior knowledge of the tree\u27s shape. Previously known load balancing algorithms either require sending a message for each tree node or they only work efficiently for large search trees. This paper introduces new randomized dynamic load balancing algorithms for {\em tree structured computations}, a generalization of backtrack search.These algorithms only need to communicate when necessary and have an asymptotically optimal scalability for many important cases. They work work on hypercubes, butterflies, meshes and many other architectures

Simple and Optimal Randomized Fault-Tolerant Rumor Spreading

We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of $O(\log n)$ when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not {time-efficient} or require intricate preprocessing steps plus synchronization).Comment: This is the author-generated version of a paper which is to appear in Distributed Computing, Springer, DOI: 10.1007/s00446-014-0238-z It is available online from http://link.springer.com/article/10.1007/s00446-014-0238-z This version contains some new results (Section 6

On the Benefit of Virtualization: Strategies for Flexible Server Allocation

Virtualization technology facilitates a dynamic, demand-driven allocation and migration of servers. This paper studies how the flexibility offered by network virtualization can be used to improve Quality-of-Service parameters such as latency, while taking into account allocation costs. A generic use case is considered where both the overall demand issued for a certain service (for example, an SAP application in the cloud, or a gaming application) as well as the origins of the requests change over time (e.g., due to time zone effects or due to user mobility), and we present online and optimal offline strategies to compute the number and location of the servers implementing this service. These algorithms also allow us to study the fundamental benefits of dynamic resource allocation compared to static systems. Our simulation results confirm our expectations that the gain of flexible server allocation is particularly high in scenarios with moderate dynamics

Unifying mesh- and tree-based programmable interconnect

We examine the traditional, symmetric, Manhattan mesh design for field-programmable gate-array (FPGA) routing along with tree-of-meshes (ToM) and mesh-of-trees (MoT) based designs. All three networks can provide general routing for limited bisection designs (Rent's rule with p<1) and allow locality exploitation. They differ in their detailed topology and use of hierarchy. We show that all three have the same asymptotic wiring requirements. We bound this tightly by providing constructive mappings between routes in one network and routes in another. For example, we show that a (c,p) MoT design can be mapped to a (2c,p) linear population ToM and introduce a corner turn scheme which will make it possible to perform the reverse mapping from any (c,p) linear population ToM to a (2c,p) MoT augmented with a particular set of corner turn switches. One consequence of this latter mapping is a multilayer layout strategy for N-node, linear population ToM designs that requires only /spl Theta/(N) two-dimensional area for any p when given sufficient wiring layers. We further show upper and lower bounds for global mesh routes based on recursive bisection width and show these are within a constant factor of each other and within a constant factor of MoT and ToM layout area. In the process we identify the parameters and characteristics which make the networks different, making it clear there is a unified design continuum in which these networks are simply particular regions

Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

The Predicted-Deletion Dynamic Model: Taking Advantage of ML Predictions, for Free

The main bottleneck in designing efficient dynamic algorithms is the unknown nature of the update sequence. In particular, there are some problems, like 3-vertex connectivity, planar digraph all pairs shortest paths, and others, where the separation in runtime between the best partially dynamic solutions and the best fully dynamic solutions is polynomial, sometimes even exponential. In this paper, we formulate the predicted-deletion dynamic model, motivated by a recent line of empirical work about predicting edge updates in dynamic graphs. In this model, edges are inserted and deleted online, and when an edge is inserted, it is accompanied by a "prediction" of its deletion time. This models real world settings where services may have access to historical data or other information about an input and can subsequently use such information make predictions about user behavior. The model is also of theoretical interest, as it interpolates between the partially dynamic and fully dynamic settings, and provides a natural extension of the algorithms with predictions paradigm to the dynamic setting. We give a novel framework for this model that "lifts" partially dynamic algorithms into the fully dynamic setting with little overhead. We use our framework to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems. In particular, we design algorithms that have amortized update time that scales with a partially dynamic algorithm, with high probability, when the predictions are of high quality. On the flip side, our algorithms do no worse than existing fully-dynamic algorithms when the predictions are of low quality. Furthermore, our algorithms exhibit a graceful trade-off between the two cases. Thus, we are able to take advantage of ML predictions asymptotically "for free.'

05361 Abstracts Collection -- Algorithmic Aspects of Large and Complex Networks

From 04.09.05 to 09.09.05, the Dagstuhl Seminar 05361 ``Algorithmic Aspects of Large and Complex Networks\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available