Nearly Linear Time Minimum Spanning TreeMaintenance for Transient Node Failures

Given a 2-node connected, real weighted, and undirected graph $G=(V,E)$, with $n$ nodes and $m$ edges, and given a minimum spanning tree (MST) $T=(V,E_T)$ of $G$, we study the problem of finding, for every node $v \in V$, a set of replacement edges which can be used for constructing an MST of $G-v$ (i.e., the graph $G$ deprived of $v$ and all its incident edges). We show that this problem can be solved on a pointer machine in ${\cal O}(m \cdot \alpha(m,n))$ time and ${\cal O}(m)$ space, where $\alpha$ is the functional inverse of Ackermann's function. Our solution improves over the previously best known ${\cal O}(\min\{m \cdot \alpha(n,n), m + n \log n\})$ time bound, and allows us to close the gap existing with the fastest solution for the edge-removal version of the problem (i.e., that of finding, for every edge $e \in E_T$, a replacement edge which can be used for constructing an MST of $G-e=(V,E \backslash \{e\})$). Our algorithm finds immediate application in maintaining MST-based communication networks undergoing temporary node failures. Moreover, in a distributed environment in which nodes are managed by selfish agents, it can be used to design an efficient, truthful mechanism for building an MS

Connectivity Oracles for Graphs Subject to Vertex Failures

We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_{\star}$ failed vertices in $\tilde{O}(d^3)$ time and thereafter answers connectivity queries in $O(d)$ time. It occupies space $O(d_{\star} m\log n)$. We develop a randomized Monte Carlo version of our data structure with update time $\tilde{O}(d^2)$, query time $O(d)$, and space $\tilde{O}(m)$ for any failure bound $d\le n$. This is the first connectivity oracle for general graphs that can efficiently deal with an unbounded number of vertex failures. We also develop a more efficient Monte Carlo edge-failure connectivity oracle. Using space $O(n\log^2 n)$, $d$ edge failures are processed in $O(d\log d\log\log n)$ time and thereafter, connectivity queries are answered in $O(\log\log n)$ time, which are correct w.h.p. Our data structures are based on a new decomposition theorem for an undirected graph $G=(V,E)$, which is of independent interest. It states that for any terminal set $U\subseteq V$ we can remove a set $B$ of $|U|/(s-2)$ vertices such that the remaining graph contains a Steiner forest for $U-B$ with maximum degree $s$

Linear Time Distributed Swap Edge Algorithms

In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2-edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If one tree edge e = {x, y} fails, the communication network will be disconnected. However, since X is 2-edge connected, communication can be restored by replacing e by non-tree edge e′, called a swap edge of e, whose ends lie in different components of T − e. Of all possible swap edges of e, we would like to choose the best, as defined by the application. The all best swap edges problem is to identify the best swap edge for every tree edge, so that in case of any edge failure, the best swap edge can be activated quickly. There are solutions to this problem for a number of cases in the literature. A major concern for all these solutions is to minimize the number of messages. However, especially in fault-transient environments, time is a crucial factor. In this paper we present a novel technique that addresses this problem from a time perspective; in fact, we present a distributed solution that works in linear time with respect to the height h of T for a number of differentcriteria, while retaining the optimal number of messages. To the best of our knowledge, all previous solutions solve the problem in O(h^2) time in the cases we consider

The Pan-STARRS Moving Object Processing System

We describe the Pan-STARRS Moving Object Processing System (MOPS), a modern software package that produces automatic asteroid discoveries and identifications from catalogs of transient detections from next-generation astronomical survey telescopes. MOPS achieves > 99.5% efficiency in producing orbits from a synthetic but realistic population of asteroids whose measurements were simulated for a Pan-STARRS4-class telescope. Additionally, using a non-physical grid population, we demonstrate that MOPS can detect populations of currently unknown objects such as interstellar asteroids. MOPS has been adapted successfully to the prototype Pan-STARRS1 telescope despite differences in expected false detection rates, fill-factor loss and relatively sparse observing cadence compared to a hypothetical Pan-STARRS4 telescope and survey. MOPS remains >99.5% efficient at detecting objects on a single night but drops to 80% efficiency at producing orbits for objects detected on multiple nights. This loss is primarily due to configurable MOPS processing limits that are not yet tuned for the Pan-STARRS1 mission. The core MOPS software package is the product of more than 15 person-years of software development and incorporates countless additional years of effort in third-party software to perform lower-level functions such as spatial searching or orbit determination. We describe the high-level design of MOPS and essential subcomponents, the suitability of MOPS for other survey programs, and suggest a road map for future MOPS development.Comment: 57 Pages, 26 Figures, 13 Table

An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner

A tree sigma-spanner of a positively real-weighted n-vertex and m-edge undirected graph G is a spanning tree T of G which approximately preserves (i.e., up to a multiplicative stretch factor sigma) distances in G. Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient edge failure in T, the overall effort that has to be afforded to rebuild a new tree spanner (i.e., computational costs, set-up of new links, updating of the routing tables, etc.) can be rather prohibitive. To circumvent this drawback, an effective alternative is that of associating with each tree edge a best possible (in terms of resulting stretch) swap edge -- a well-established approach in the literature for several other tree topologies. Correspondingly, the problem of computing all the best swap edges of a tree spanner is a challenging algorithmic problem, since solving it efficiently means to exploit the structure of shortest paths not only in G, but also in all the scenarios in which an edge of T has failed. For this problem we provide a very efficient solution, running in O(n^2 log^4 n) time, which drastically improves (almost by a quadratic factor in n in dense graphs!) on the previous known best result

04091 Abstracts Collection -- Data Structures

From 22.02. to 27.02.2004, Dagstuhl Seminar "Data Structures" 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 are put together in this paper. The first section describes the seminar topics and goals in general

Managing dynamic groups in QoS and overlay multicasting

Multicasting has been the most popular mechanism for supporting group communication, wherein group members communicate through a multicast data distribution tree that spans all the members of the group. In a dynamic multicast session, members join/leave the group using graft/prune mechanisms, based on locally optimal paths, which would eventually degenerate the quality of the multicast tree. Therefore, efficient mechanisms need to be invoked periodically to maintain the cost of the multicast tree near optimal. However, tree maintenance would result in service disruption for the session. Therefore, there exists a trade-off between minimizing tree cost and minimizing service disruption. The goal of this dissertation is to develop and analyze a set of efficient tree maintenance techniques that aim to balance this tradeoff in QoS and overlay multicasting. To achieve this goal, the dissertation makes three key contributions. First, the design of scalable protocols, viz. tree migration and tree evolution, for maintaining QoS multicast trees. Second, the design of an efficient strategy, called partial protection approach, and its implementation methods for member join problem with path reliability being a QoS constraint. Third, the design of an efficient tree maintenance algorithm, based on the idea of mesh-tree interactions, for end-system based overlay multicasting. The proposed tree maintenance solutions have been evaluated and analyzed through a combination of simulation and analytical studies. The studies show that the proposed solutions indeed achieve a good balance between tree cost and service disruption competitively

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Mathematical modelling of gas flow networks in pellet induratlon systems

The objective of this research is to develop a simulation software tool, GASFLO, which should evaluate pressure, flow and temperature distributions of process gas in pellet induration system networks. Pellet induration systems are complex industrial systems composed of heterogenous components. The magnitude of gas through leaks i.e. the air entering or leaving the system from the points other than the known exits, is substantial and it adversely effects the performance of induration process. These leaks are very difficult to measure because of the hostile environment in the plant. The modelling of such industrial systems requires a notable amount of experimentation so the tool has been designed to enable the user modeller to change the component models and solution algorithms easily. The conventional methods for flow network simulation are based on process centred approach, mostly composed of homogeneous components. For ease of computation, the non-pipe elements are modelled with an approximate linear or non-linear generic equation, whose coefficients can simulate different states of the element. The resulting set of non-linear equations is linearised and solved simultaneously using some iterative method. By contrast, GASFLO is based on device centred or unit based approach, and uses a two level hierarchical solution algorithm. The pellet induration system network is first idealised into a connected graph of streams (sets of serially connected components) and nodes. At the top or coordination level the flow and pressure distributions satisfying the Kirchhoff's laws are evaluated for the connected graph. At the lower or component level the exact mathematical models of components ale computed, in order of their occurrence in respective streams, using coordination variables as parameters. The converged flows are used for the temperature computation. The solution algorithm requires partitioning of the connected graph into forest and coforest structures, for which secondary algorithms have been developed using specific heuristics relevant to the pellet induration systems. The rigorous application of software engineering techniques for the design and implementation of software, enabled the resolution of the complexity of the modelled system, embedded the characteristics of 'quality software' into the resulting code and benefits from object orientation, even though it is implemented in standard FORTRAN 77. GASFLO predicted results are in a good agreement with the measured results, it has been validated for a real life pellet induration system. It has been applied to simulate several practical scenarios, like addition of extra wind boxes to the zones and to determine how the plant production can be increased by certain ratio, such simulations were not feasible otherwise. GASFLO takes less than a minute to simulate a real-life pellet induration system on a 486 PC. The combined simulation with an other software tool, INDSYS, which evaluates the heat distribution in the solids, is also feasible

Integration of tools for the Design and Assessment of High-Performance, Highly Reliable Computing Systems (DAHPHRS), phase 1

Systems for Space Defense Initiative (SDI) space applications typically require both high performance and very high reliability. These requirements present the systems engineer evaluating such systems with the extremely difficult problem of conducting performance and reliability trade-offs over large design spaces. A controlled development process supported by appropriate automated tools must be used to assure that the system will meet design objectives. This report describes an investigation of methods, tools, and techniques necessary to support performance and reliability modeling for SDI systems development. Models of the JPL Hypercubes, the Encore Multimax, and the C.S. Draper Lab Fault-Tolerant Parallel Processor (FTPP) parallel-computing architectures using candidate SDI weapons-to-target assignment algorithms as workloads were built and analyzed as a means of identifying the necessary system models, how the models interact, and what experiments and analyses should be performed. As a result of this effort, weaknesses in the existing methods and tools were revealed and capabilities that will be required for both individual tools and an integrated toolset were identified