Implementations and Experimental Studies of Dynamic Graph Algorithms

In dynamic graph algorithms the following provide-or-bound problem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements from S testing for membership in R, either (i) provide an element of R, or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dynamic graph algorithms by a factor of O(log n). For example, it improves the time per update for fully dynamic connectivity from O(log3n) to O(log2n). © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 369–379 (1997)

A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms for graph problems that are solvable in polynomial time by a static algorithm. However, while there is a large body of theoretical work on efficient dynamic graph algorithms, a lot of these algorithms were never implemented and empirically evaluated.In this work, we consider the fully dynamic edge orientation problem, also called fully dynamic Δ-orientation problem, which is to maintain an orientation of the edges of an undirected graph such that the out-degree is low. If edges are inserted or deleted, one may have to flip the orientation of some edges in order to avoid vertices having a large out-degree. While there has been theoretical work on dynamic versions of this problem, currently there is no experimental evaluation available. In this work, we close this gap and engineer a range of new dynamic edge orientation algorithms as well as algorithms from the current literature. The most successful newly proposed algorithms in this paper are based on repeatedly swapping edges with smallest degree neighbors and based on breadth-first search. Moreover, we evaluate these algorithms on real-world dynamic graphs. Generally, these algorithms outperform the algorithms currently proposed in the literature. The best algorithm considered in this paper in terms of quality, based on a simple breadth-first search, computes the optimum result more than 90% of the instances and is on average only 2.4% worse than the optimum solution.*The full version of the paper can be accessed at https://arxiv.org/abs/2301.06968

Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, there exist many recent randomized results that aim to provide a guarantee stronger than amortized expected. The strongest possible guarantee for a randomized algorithm is that it is always correct (Las Vegas) and has high-probability worst-case update time, which gives a bound on the time for each individual operation that holds with high probability. In this article, we present the first polylogarithmic high-probability worst-case time bounds for the dynamic spanner and the dynamic maximal matching problem. (1) For dynamic spanner, the only known o ( n ) worst-case bounds were O ( n 3/4 ) high-probability worst-case update time for maintaining a 3-spanner and O ( n 5/9 ) for maintaining a 5-spanner. We give a O (1) k log 3 ( n ) high-probability worst-case time bound for maintaining a ( 2k-1 )-spanner, which yields the first worst-case polylog update time for all constant k . (All the results above maintain the optimal tradeoff of stretch 2k-1 and Õ( n 1+1/k ) edges.) (2) For dynamic maximal matching, or dynamic 2-approximate maximum matching, no algorithm with o(n) worst-case time bound was known and we present an algorithm with O (log 5 ( n )) high-probability worst-case time; similar worst-case bounds existed only for maintaining a matching that was (2+ϵ)-approximate, and hence not maximal. Our results are achieved using a new approach for converting amortized guarantees to worst-case ones for randomized data structures by going through a third type of guarantee, which is a middle ground between the two above: An algorithm is said to have worst-case expected update time ɑ if for every update σ, the expected time to process σ is at most ɑ. Although stronger than amortized expected, the worst-case expected guarantee does not resolve the fundamental problem of amortization: A worst-case expected update time of O(1) still allows for the possibility that every 1/ f(n) updates requires ϴ ( f(n) ) time to process, for arbitrarily high f(n) . In this article, we present a black-box reduction that converts any data structure with worst-case expected update time into one with a high-probability worst-case update time: The query time remains the same, while the update time increases by a factor of O (log 2(n) ). Thus, we achieve our results in two steps: (1) First, we show how to convert existing dynamic graph algorithms with amortized expected polylogarithmic running times into algorithms with worst-case expected polylogarithmic running times. (2) Then, we use our black-box reduction to achieve the polylogarithmic high-probability worst-case time bound. All our algorithms are Las-Vegas-type algorithms.

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-ε)-approximation schemes for various versions of the multicommodity flow problem. In particular, if ε is moderately small and the size of every number used in the input instance is polynomially bounded, the running times of our algorithms match -- up to poly-logarithmic factors and some provably optimal terms -- the Ω(mn) flow-decomposition barrier for single-commodity flow.

In 1999, Brodal and Fagerberg (BF) gave an algorithm for maintaining a low outdegree orientation of a dynamic uniformly sparse graph. Specifically, for a dynamic graph on n -vertices, with arboricity bounded by ɑ at all times, the BF algorithm supports edge updates in O (log n ) amortized update time, while keeping the maximum outdegree in the graph bounded by O ( ɑ ). Such an orientation provides a basic data structure for uniformly sparse graphs, which found applications to several dynamic graph algorithms, including adjacency queries and labeling schemes, maximal and approximate matching, approximate vertex cover, forest decomposition, and distance oracles. A significant weakness of the BF algorithm is the possible temporary blowup of the maximum outdegree, following edge insertions. Although BF eventually reduces all outdegrees to O ( ɑ ), some vertices may reach an outdegree of Ω( n ) during the process, and hence local memory usage at the vertices, which is an important quality measure in distributed systems, cannot be bounded. We show how to modify the BF algorithm to guarantee that the outdegrees of all vertices are bounded by O ( ɑ ) at all times, without hurting any of its other properties and present an efficient distributed implementation of the modified algorithm. This provides the first representation of distributed networks in which the local memory usage at all vertices is bounded by the arboricity (which is essentially the average degree of the densest subgraph) rather than the maximum degree. For settings where there is no strict limitation on the local memory, one may take the temporary outdegree blowup to the extreme and allow a permanent outdegree blowup. This allows us to address the second significant weakness of the BF algorithm—its inherently global nature: An insertion of an edge ( u,v ) may trigger changes in the orientations of edges that are arbitrarily far away from u and v . Such a non-local scheme may be prohibitively expensive in various practical applications. We suggest an alternative local scheme, which does not guarantee any outdegree bound on the vertices, yet is just as efficient as the BF scheme for some of the aforementioned applications. For example, we obtain a local dynamic algorithm for maintaining a maximal matching with sub-logarithmic update time in uniformly sparse networks, providing an exponential improvement over the state of the art in this context. We also present a distributed implementation of this scheme and some of its applications.

The three-in-a-tree problem is to determine if a simple undirected graph contains an induced subgraph which is a tree connecting three given vertices. Based on a beautiful characterization that is proved in more than twenty pages, Chudnovsky and Seymour [Combinatorica 2010] gave the previously only known polynomial-time algorithm, running in $O(mn^2)$ time, to solve the three-in-a-tree problem on an $n$-vertex $m$-edge graph. Their three-in-a-tree algorithm has become a critical subroutine in several state-of-the-art graph recognition and detection algorithms. In this paper we solve the three-in-a-tree problem in $\tilde{O}(m)$ time, leading to improved algorithms for recognizing perfect graphs and detecting thetas, pyramids, beetles, and odd and even holes. Our result is based on a new and more constructive characterization than that of Chudnovsky and Seymour. Our new characterization is stronger than the original, and our proof implies a new simpler proof for the original characterization. The improved characterization gains the first factor $n$ in speed. The remaining improvement is based on dynamic graph algorithms.

Data token heuristic scheduling of the Kalman algorithm onto a message-passing multiprocessor system

Recently, Wireless Sensor Networks (WSNs) have been extensively employed in several tactical applications out of which target detection, habit monitoring, and earthquake monitoring. The open characteristic nature of WSNs makes it vulnerable to be attacked by an eavesdropper who aims at disrupting the network operation or access confidential information. Consequently, ensuring the security and privacy in WSNs is considered an essential issue and definitely cannot be left without proper investigations. There are two types of threats that may occur for the WSNs privacy, that are, contextual and content privacy. Location privacy is considered an example of contextual privacy. In this paper, three source privacy protection schemes, which are based on clustering methodology, are proposed to protect contextual privacy. These schemes are dynamic shortest path (DSP) scheme, dynamic tree (DT) scheme, and hybrid scheme. Interestingly, a grid-based clustering technique is adopted to divide the network into several square clusters. Matlab simulations are used to evaluate the performance of the three proposed schemes in terms of latency, energy consumption, and safety period. The results undoubtedly confirm the effectiveness of the proposed schemes. Very high safety period is achieved and an adequate amount of energy is consumed. Furthermore, acceptable latency is achieved when compared to the shortest path scheme.

Dear SCPE Reader, We present a selection of papers which are extensions of papers presented at the 7-th International Symposium on Parallel and Distributed Computing, 1–5 July 2008, in Krakow, Poland. The motivation for publishing the selection in the SCPE Journal was, on the one hand, to present the flavour of the research reported at the conference and on the other hand to present some of the most relevant topics currently focused on the research on parallel and distributed computing in general. The selection contains only 6 papers out of about 60 presented at the conference, and thus, is far from covering all relevant topics represented at the ISPDC 2008. This is because not all of the invited authors were patient enough to accept a fairly long paper publishing process. Nevertheless, we hope that the presented papers will bring you closer to the research covered by the ISPDC conferences and will encourage you to participate in future ISPDC editions. The first paper ``The Impact of Workload Variability on Load Balancing Algorithms'' is by Marta Beltran and Antonio Guzman from King Juan Carlos University in Spain. It concerns an important topic of load balancing in cluster systems, namely adaptativity of the load balancing algorithms to changes of the workload in the system. Adequate accounting for additional load in the hosting system is of great relevance for correct optimization effects. The paper presents a thorough formal analysis of the workload variability metrics and their influence on the quality of load balancing algorithms. Four basic activities appearing in load balancing algorithms are identified, and based on them some algorithmic solutions are proposed to correctly deal with workload variability in system load balancing. The problem of dynamic load balancing algorithms robustness has been discussed. Two different robustness metrics sensitive to the applied type of opimization: local task-oriented or a global one enable selecting task remote execution or migration as load balancing operations. The proposed approach is illustrated with experiments. The second paper ``Model-Driven Engineering and Formal Validation of High-Performance Embedded Systems'' is by Abdoulaye Gamatie, Eric Rutten, Huafeng Yu, Pierre Boulet, Jean-Luc Dekeyser, from University of Lille and INRIA in France. The paper is concerned with a very advanced methodology of designing correct parallel embedded systems for intensive data-parallel computing. In their previous research, the authors of the paper designed the GASPARD embedded system design framework. It is based on the hardware/software co-design approach through model-driven engineering. The framework is based on an UML-like model specification language in which hardware and software elements are modelled using a component approach with special mechanisms for repetitive structures. This paper tries to combine the modelling framework of GASPARD with the mechanisms of synchronous languages to achieve design verifiability provided for such languages. The paper shows how GASPARD models can be translated into synchronous models based on data flow equations in order to formally check their correctness. The proposed approach is illustrated with an example of a video processing system. The third paper ``Relations Between Several Parallel Computational Models'' is by Stephan Bruda and Yuanqiao Zhang from Bishop’s University in Canada. The paper is concerned with theoretical aspects of shared memory systems described by the parallel random access machine PRAM model and aims in studying performance properties of different types of PRAM systems. The attention is focussed on analysing the computational power of two more sophisticated PRAM models (Combining CRCW and Broadcast Selective Reduction), which include data reduction in case of concurrent writes. The paper shows that these two models have equivalent computational power, which is a new result comparing the existing literature. The performance of both models applied to reconfigurable multiple bus machines was studied as a possible architectural solution for current VLSI processor implementations. It was shown that in such systems under reasonable assumptions concurrent-write does not enhance performance comparing the exclusive-write model. Another result important for the VLSI technology is that the Combining CRCW PRAM model (in which data of concurrent writes are arthmetically or logically combined before write) and the exclusive-write on directed reconfigurable busses perform in equivalent way under strong real-time requirements. The fourth paper ``Experiences with Mesh-Like Computations Using Prediction Binary Trees'' is by Gennaro Cordasco, Biagio Cosenza, Rosario de Chiara, Ugo Erra and Vittorio Scarano from the University ``degli Studi'' of Salerno and the University ``degli Studi della Biasilicata'' of Potenza in Italy. The paper concerns optimization methods for mesh-like computations in clusters of processors. The computations are perfomed assuming a phase-like program execution control using a tiling approach which reduces inter-processor communication. A temporal coherence is also assumed, which means that task sizes provide similar execution times in consecutive phases. Temporary coherent computations are structured in a Prediction Binary Tree, in which leaves represent computing tiles to be mapped to processors. A phase-by-phase semi-static load balancing is introduced to the scheduling algorithm. The scheduling algorithm is equipped with a predictor, which estimates the computation time of next phase tiles based on previous execution times and modifies the tiles to achieve balanced execution in phases. For this, two heuristics are used to leverage on data locality in processors. The proposed approach is illustrated by the example of interactive rendering with Parallel Ray Tracing algorithm. The fifth paper ``The Influence of the IBM pSeries Servers Virtualization Mechanism on Dynamic Resource Allocation in AIX 5L'' is by Maciej Mlynski from ASpartner Limited in Poland. The paper concerns a very up-to-date problem of system virtualization and presents the results of research carried on IBM pSeries servers. IBM is strongly developing the virtualization technique especially on IBM pSeries servers enabling an improved and flexible sharing of system resources between applications. The paper investigates novel facilities for dynamic resource management such as micro-partitioning and partition load manager. They enable dynamic creation of workload logical partitions of system resources and their dynamic mangement. It includes run-time resource re-alocation between logical partitions including setting of sharing specifications as well as run-time adding/removing/setting parameters of resources in the system. It remains an open question how to properly tune parameters of the operating system using the provided virtualization facilities to obtain the best efficiency for a given application program. The paper presents the results of experiments which study the effects of tuning the disk subsystem parameters under the IBM AIX 5L operating system with the use of the provided virtualization facilities on the resulting application execution performance. The results show that even small deterioration in the resource pool status requires an immediate adaptation of the operating system parameters to maintain the required performance. The sixth paper ``HeteroPBLAS: A Set of Parallel Basic Linear Algebra Subprograms Optimized for Heterogeneous Computational Clusters'' is by Ravi Reddy, Alexey Lastovetsky and Pedro Alonso from University College Dublin in Ireland and Polytechnic University of Valencia in Spain. The paper concerns the methodology for parallelization of linear algebra computations for execution in heterogeneous cluster environments. The design of the HeteroPBLAS library (Parallel Basic Linear Algebra Subprograms) for heterogeneous computational clusters is presented. The main contribution of the paper is the automation of the parallelization and optimization of the PBLAS, which is done by means of a special user interface and the underlying set of functions. An important element is here a performance model that is based on program code instrumentation, which determines parameters of the application and the executive heterogeneous platform relevant for execution performance of parallel code. The parameter values specified for or returned by execution of the performance model functions are next used for generation and optimal mapping of the parallel code of the library subroutines. The proposed approach is illustrated by experimental results of execution of optimized HeteroPBLAS programs on homogeneous and heterogeneous computing clusters. Marek Tudruj

We study differentially private algorithms for analyzing graph databases in the challenging setting of continual release with fully dynamic updates, where edges are inserted and deleted over time, and the algorithm is required to update the solution at every time step. Previous work has presented differentially private algorithms for many graph problems that can handle insertions only or deletions only (called partially dynamic algorithms) and obtained some hardness results for the fully dynamic setting. The only algorithms in the latter setting were for the edge count, given by Fichtenberger, Henzinger, and Ost (ESA '21), and for releasing the values of all graph cuts, given by Fichtenberger, Henzinger, and Upadhyay (ICML '23). We provide the first differentially private and fully dynamic graph algorithms for several other fundamental graph statistics (including the triangle count, the number of connected components, the size of the maximum matching, and the degree histogram), analyze their error, and show strong lower bounds on the error for all algorithms in this setting. Previously, only lower bounds for purely differentially private algorithms were known; our lower bounds give an exponential improvement in terms of the dependence on the number of time steps, while applying to algorithms satisfying pure as well as approximate differential privacy. We study two variants of edge differential privacy for fully dynamic graph algorithms: event-level and item-level. Under the former notion, two graph database update sequences are considered neighboring if, roughly speaking, they differ in at most one update; under the latter notion, they can differ only in updates pertaining to one edge. Differential privacy requires that for any two neighboring inputs, the output distributions of the algorithm are close. We give upper and lower bounds on the error of both---event-level and item-level---fully dynamic algorithms for several fundamental graph problems. No fully dynamic algorithms that are private at the item-level (the more stringent of the two notions) were known before. In the case of item-level privacy, for several problems, our algorithms match our lower bounds.

Through we do some research on the key technology and implementation of the air product simulation resource model library, we propose a general system framework, the solid modeling method of the components and parts, the design of the parameter table and the model library integration and application. With these key technologies, we design and develop three-dimensional modeling library system, CATIA taken as a platform.

The contributions of this paper are both of theoretical and of experimental nature. From the experimental point of view, we conduct an empirical study on some dynamic connectivity algorithms which where developed recently. In particular, the following implementations were tested and compared with simple algorithms: simple sparsification by Eppstein et al. and the recent randomized algorithm by Henzinger and King. In our experiments, we considered both random and non-random inputs. Moreover, we present a simplified variant of the algorithm by Henzinger and King, which for random inputs was always faster than the original implementation. For non-random inputs, simple sparsification was the fastest algorithm for small sequences of updates; for medium and large sequences of updates, the original algorithm by Henzinger and King was faster.From the theoretical point of view, we analyze the average case running time of simple sparsification and prove that for dynamic random graphs its logarithmic overhead vanishes.

This paper solves a longstanding open problem in fully dynamic algorithms: We present the first fully dynamic algorithms that maintain connectivity, bipartiteness, and approximate minimum spanning trees in polylogarithmic time per edge insertion or deletion. The algorithms are designed using a new dynamic technique that combines a novel graph decomposition with randomization. They are Las-Vegas type randomized algorithms which use simple data structures and have a small constant factor. Let n denote the number of nodes in the graph. For a sequence of Ω( m 0 ) operations, where m 0 is the number of edges in the initial graph, the expected time for p updates is O ( p log 3 n ) (througout the paper the logarithms are based 2) for connectivity and bipartiteness. The worst-case time for one query is O (log n /log log n ). For the k -edge witness problem (“Does the removal of k given edges disconnect the graph?”) the expected time for p updates is O ( p log 3 n ) and the expected time for q queries is O ( qk log 3 n ). Given a graph with k different weights, the minimum spanning tree can be maintained during a sequence of p updates in expected time O ( pk log 3 n ). This implies an algorithm to maintain a 1 + ε-approximation of the minimum spanning tree in expected time O (( p log 3 n log U )/ε) for p updates, where the weights of the edges are between 1 and U .

The Media Broadcast industry has evolved from Serial Digital Interface (SDI) based infrastructures to IP networks. While IP based video broadcast is well established in the data plane, the use of IP networks to transport media flows still poses challenges in terms of resource management and orchestration. SDN based orchestration architectures have emerged in the industry that use SDN to route the media flows of a broadcast service across the provider IP network. Several approaches to multimedia flow routing in IP based SDN networks have been proposed in the context of streaming applications over the Internet. These range from model based linear optimization solutions that have high complexity to simple shortest path based routing heuristics with either static or dynamic link costs. More recently model-free optimization methods such as Deep Reinforcement Learning (DRL) have been proposed for routing and Traffic Engineering of multimedia flows in SDN networks. The media broadcast scenario however has specific requirements, with services like Master Control Room operation and Live broadcasting of events, and it has been rarely addressed in the literature. In this work we propose a DRL based routing method for this scenario and compare it to static and dynamic link cost algorithms based on Dijkstra shortest paths. This is to our knowledge the first work to follow this approach in the context of Media Broadcast services in IP infrastructures. The algorithm is designed considering the specifications and capabilities of one of the leading SDN orchestrators in the market and considers the more common Service Level Agreement requirements in the industry. Three different DRL algorithms are implemented and compared and we evaluate them using a real service provider network topology. The results indicate that DRL based routing is applicable in real production scenarios and that it achieves considerable performance gains when compared to the static and dynamic link cost shortest path algorithms commonly used today.

An integrated multiple autonomous underwater vehicle (multi-AUV) dynamic task assignment and path planning algorithm is proposed by combing the improved self-organizing map (SOM) neural network and...