Tarjan's Algorithm Research Articles

Navigation-Oriented Topological Model Construction Algorithm for Complex Indoor Space

Indoor space information is the basis of indoor location services such as indoor navigation, path planning, emergency evacuation, etc. Focusing on indoor navigation needs, this paper proposes a fast construction algorithm for a complex indoor space topology model based on disjoint set for the problem of lacking polygon description and topological relationship expression of indoor space entity objects in building plan drawings. Firstly, the Tarjan algorithm is used for identifying the hanging edges existing in the indoor space. Secondly, each edge is stored as two different edges belonging to two adjacent polygons that share the edge. A ring structure is introduced to judge the geometric position of walls, and then an efficient disjoint set algorithm is used to perform set merging. After that, disjoint set is queried to obtain all indoor space contours and external boundary contours, thereby the complete indoor space topological relationship at multiple levels is established. Finally, the connectivity theory of graph is used for solving the problem of a complex isolated polygon in topology information generation. The experimental results show that the proposed algorithm has generality to efficiently complete the automatic construction of a topological model for complex scenarios, and effectively acquire and organize indoor space information, thus providing a good spatial cognition mode for indoor navigation.

Parallel Strong Connectivity Based on Faster Reachability

Computing strongly connected components (SCC) is among the most fundamental problems in graph analytics. Given the large size of today's real-world graphs, parallel SCC implementation is increasingly important. SCC is challenging in the parallel setting and is particularly hard on large-diameter graphs. Many existing parallel SCC implementations can be even slower than Tarjan's sequential algorithm on large-diameter graphs. To tackle this challenge, we propose an efficient parallel SCC implementation using a new parallel reachability approach. Our solution is based on a novel idea referred to as vertical granularity control (VGC). It breaks the synchronization barriers to increase parallelism and hide scheduling overhead. To use VGC in our SCC algorithm, we also design an efficient data structure called the parallel hash bag. It uses parallel dynamic resizing to avoid redundant work in maintaining frontiers (vertices processed in a round). We implement the parallel SCC algorithm by Blelloch et al. (J. ACM, 2020) using our new parallel reachability approach. We compare our implementation to the state-of-the-art systems, including GBBS, iSpan, Multi-step, and our highly optimized Tarjan's (sequential) algorithm, on 18 graphs, including social, web, k-NN, and lattice graphs. On a machine with 96 cores, our implementation is the fastest on 16 out of 18 graphs. On average (geometric means) over all graphs, our SCC is 6.0× faster than the best previous parallel code (GBBS), 12.8× faster than Tarjan's sequential algorithms, and 2.7× faster than the best existing implementation on each graph. We believe that our techniques are of independent interest. We also apply our parallel hash bag and VGC scheme to other graph problems, including connectivity and least-element lists (LE-lists). Our implementations improve the performance of the state-of-the-art parallel implementations for these two problems.

SafeDrop: Detecting Memory Deallocation Bugs of Rust Programs via Static Data-flow Analysis

Rust is an emerging programming language that aims to prevent memory-safety bugs. However, the current design of Rust also brings side effects, which may increase the risk of memory-safety issues. In particular, it employs ownership-based resource management and enforces automatic deallocation of unused resources without using the garbage collector. It may therefore falsely deallocate reclaimed memory and lead to use-after-free or double-free issues. In this article, we study the problem of invalid memory deallocation and propose SafeDrop , a static path-sensitive data-flow analysis approach to detect such bugs. Our approach analyzes each function of a Rust crate iteratively in a flow-sensitive and field-sensitive way. It leverages a modified Tarjan algorithm to achieve scalable path-sensitive analysis and a cache-based strategy for efficient inter-procedural analysis. We have implemented our approach and integrated it into the Rust compiler. Experiment results show that the approach can successfully detect all such bugs in our experiments with a limited number of false positives and incurs a very small overhead compared to the original compilation time.

A Multi-path Nonoverlapping Routing Algorithm for Deterministic Networking

Deterministic Networking (DetNet) is a new network architecture proposed by IETF DetNet working group for industrial Internet of Things and other application scenarios. Its communication service with high reliability and low delay needs multi-path nonoverlapping routing algorithm. Because it is different from existing routing algorithms on the Internet, it is an important subject to study routing algorithms that meet requirements of DetNet. Based on routing characteristics of DetNet, we studied a multi-routing algorithm - Bhandari algorithm. Aiming at the problem that the algorithm cannot calculate nonoverlapping routes in some cases, we improve the algorithm, then we also make the improved algorithm more efficient by introducing Tarjan algorithm. The improved algorithm is verified and tested in the simulation environment and results show the effectiveness of the improved algorithm.

Almost Sure Synchronization of Multilayer Networks via Intermittent Pinning Noises: A White-Noise-Based Time-Varying Coupling

This paper is concerned with the almost sure exponential synchronization of a multilayer network which is set up on a non-strongly connected digraph that can be classified into several layers by Tarjan's algorithm. Note that, in the multilayer network, white-noise-based time-varying coupling and drift term coupling are proposed to simulate two kinds of coexisting distinguishable interactions between vertices. We develop a normal analytical framework for studying synchronization of the multilayer network. Firstly, via aperiodically intermittent pinning noises, synchronization of vertices situated on the first layer is achieved in the layered network. Secondly, under the impact of the white-noise-based time-varying coupling in diffusion term, synchronization of the vertices located in other layer networks is developed with the support of synchronization for the pinned vertices. Employing Lyapunov method, graph theory and stochastic analysis technique, a criterion of almost sure global exponential synchronization is obtained. By adopting the concepts of average noise control rate and average noise control period proposed recently, we lessen the conservativeness of the conditions restricted on aperiodically intermittent noise control to optimize our results. Furthermore, an application to a class of Chua's circuits is exhibited in detail. In the end, we provide a numerical example to verify the validity of the theoretical results.

A Deterministic-Path Routing Algorithm for Tolerating Many Faults on Very-Large-Scale Network-on-Chip

Very-large-scale network-on-chip (VLS-NoC) has become a promising fabric for supercomputers, but this fabric may encounter the many-fault problem. This article proposes a deterministic routing algorithm to tolerate the effects of many faults in VLS-NoCs. This approach generates routing tables offline using a breadth-first traversal algorithm and stores a routing table locally in each switch for online packet transmission. The approach applies the Tarjan algorithm to degrade the faulty NoC and maximizes the number of available nodes in the reconfigured NoC. In 2D NoCs, the approach updates routing tables of some nodes using the deprecated channel/node rules and avoids deadlocks in the NoC. In 3D NoCs, the approach uses a forbidden-turn selection algorithm and detour rules to prevent faceted rings and ensures the NoC is deadlock-free. Experimental results demonstrate that the proposed approach provides fault-free communications of 2D and 3D NoCs after injecting 40 faulty links. Meanwhile, it maximizes the number of available nodes in the reconfigured NoC. The approach also outperforms existing algorithms in terms of average latency, throughput, and energy consumption.

Proving the Absence of Unbounded Polymers in Rule-based Models

Rule-based languages, such as Kappa and BNGL, allow for the description of very combinatorial models of interactions between proteins. A huge (when not infinite) number of different kinds of bio-molecular compounds may arise due to proteins with multiple binding and phosphorylation sites. Knowing beforehand whether a model may involve an infinite number of different kinds of bio-molecular compounds is crucial for the modeller. On the first hand, having an infinite number of kinds of bio-molecular compounds is sometimes a hint for modelling flaws: forgetting to specify the conflicts among binding rules is a common mistake. On the second hand, it impacts the choice of the semantics for the models (among stochastic, differential, hybrid).In this paper, we introduce a data-structure to abstract the potential unbounded polymers that may be formed in a rule-based model. This data-structure is a graph, the nodes and the edges of which are labelled with patterns. By construction, every potentially unbounded polymer is associated to at least one cycle in that graph. This data-structure has two main advantages. Firstly, as opposed to site-graphs, one can reason about cycles without enumerating them (by the means of Tarjan's algorithm for detecting strongly connected components). Secondly, this data-structures may be combined easily with information coming from additional reachability analysis: the edges that are labelled with an overlap that is proved unreachable in the model may be safely discarded.

From Big-Step to Small-Step Semantics and Back with Interpreter Specialisation

We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We then specialise an interpreter with respect to a given source program to achieve a compilation of the source language to Horn clauses (an instance of the first Futamura projection). The process is described in detail for an interpreter for a subset of C, directly encoding the rules of big-step operational semantics for C. A similar translation based on small-step semantics could be carried out, but we show an approach to obtaining a small-step representation using a linear interpreter for big-step Horn clauses. This interpreter is again specialised to achieve the translation from big-step to small-step style. The linear small-step program can be transformed back to a big-step non-linear program using a third interpreter. A regular path expression is computed for the linear program using Tarjan's algorithm, and this regular expression then guides an interpreter to compute a program path. The transformation is realised by specialisation of the path interpreter. In all of the transformation phases, we use an established partial evaluator and exploit standard logic program transformation to remove redundant data structures and arguments in predicates and rename predicates to make clear their link to statements in the original source program.

Railway wagon flow routing locus pattern intelligent recognition algorithm based on SST

Purpose The operating wagon records were produced from distinct railway information systems, which resulted in the wagon routing record with the same oriental destination (OD) was different. This phenomenon has brought considerable difficulties to the railway wagon flow forecast. Some were because of poor data quality, which misled the actual prediction, while others were because of the existence of another actual wagon routings. This paper aims at finding all the wagon routing locus patterns from the history records, and thus puts forward an intelligent recognition method for the actual routing locus pattern of railway wagon flow based on SST algorithm. Design/methodology/approach Based on the big data of railway wagon flow records, the routing metadata model is constructed, and the historical data and real-time data are fused to improve the reliability of the path forecast results in the work of railway wagon flow forecast. Based on the division of spatial characteristics and the reduction of dimension in the distributary station, the improved Simhash algorithm is used to calculate the routing fingerprint. Combined with Squared Error Adjacency Matrix Clustering algorithm and Tarjan algorithm, the fingerprint similarity is calculated, the spatial characteristics are clustering and identified, the routing locus mode is formed and then the intelligent recognition of the actual wagon flow routing locus is realized. Findings This paper puts forward a more realistic method of railway wagon routing pattern recognition algorithm. The problem of traditional railway wagon routing planning is converted into the routing locus pattern recognition problem, and the wagon routing pattern of all OD streams is excavated from the historical data results. The analysis is carried out from three aspects: routing metadata, routing locus fingerprint and routing locus pattern. Then, the intelligent recognition SST-based algorithm of railway wagon routing locus pattern is proposed, which combines the history data and instant data to improve the reliability of the wagon routing selection result. Finally, railway wagon routing locus could be found out accurately, and the case study tests the validity of the algorithm. Practical implications Before the forecasting work of railway wagon flow, it needs to know how many kinds of wagon routing locus exist in a certain OD. Mining all the OD routing locus patterns from the railway wagon operating records is helpful to forecast the future routing combined with the wagon characteristics. The work of this paper is the basis of the railway wagon routing forecast. Originality/value As the basis of the railway wagon routing forecast, this research not only improves the accuracy and efficiency for the railway wagon routing forecast but also provides the further support of decision-making for the railway freight transportation organization.

Scheme for tour planning of mobile sink in wireless sensor networks

Exploiting mobile sink (MS) for data gathering in the wireless sensor networks has been extensively studied in the recent researches to address energy-hole issues, thereby facilitating balanced energy consumption among nodes and so prolonging network lifetime. However, such approaches suffer from an extended data collection delay causing buffer overflow problem. In this regard, finding the optimal number of locations (i.e. rendezvous points (RPs) where the MS sojourns for data collection), is not only of utmost importance, but also a challenging task. A novel scheme for trajectory design of MS for data collection is presented in this study. The authors' primary goal is to optimise the number of RPs and their locations to minimise the travelling length of the MS. First, they reduced the problem size by using a combination of breadth-first search and Tarjan's algorithm and then applied spectral clustering to find the optimal set of RPs to plan the tour for the MS. They have performed extensive simulations, and the results are compared with relevant existing schemes. The comparative results confirm the effectiveness of their approach in terms of the number of RPs, path length, the variance of RPs, and energy consumption per round.

The Last Circuit Breakers Identification in Hybrid AC/DC Power Grids Based on Improved Tarjan Algorithm

The last circuit breaker (LCB) protection is applied in hybrid AC/DC power grids to protect the AC/DC equipment from overvoltage threats caused by the unexpected tripping of LCBs. In this paper, an improved Tarjan algorithm is proposed to identify LCBs that correspond to the cut vertices on the path between any two vertices in the connected undirected graph. The proposed method can be applied to multiple converter valves to simultaneously identify the LCBs for each converter valve where all vertices in the connected undirected graph are traversed only once, which significantly improves the running efficiency. The real-time performance of the LCBs identification process was examined on a closed-loop simulation platform based on LabVIEW and MATLAB. The results reveal excellent capabilities of the proposed method for finding LCBs for all converter valves under various conditions of the AC field while exhibiting a lower and more stable runtime.

Застосування графів для відображення життєвого циклу сутностей під час розроблення системи опрацювання відгуків безпосередніх користувачів програмних продуктів

Важливою для безпосереднього користувача здатністю будь-якого програмного продукту є гнучкість застосування та налаштування. Проблема, описана та частково досліджена у цій науковій роботі, стосується питання забезпечення цієї гнучкості, а саме – підходів до задавання в межах програмної системи набору станів певної сутності, а також накладення обмеження на множину станів, у які згадана вище сутність може перейти, перебуваючи в одному із них. Тут і далі під правилами переходу сутності в різні стани мають на увазі обмеження множини наступних станів. Оглянуто сучасні системи для керування відгуками до програмного забезпечення, як приклад предметної області зі сутностями, які не мають наперед визначеної множини станів та переходів між ними. Проаналізовано основні переваги та недоліки аналогічних систем та їх підходу до зберігання станів. Наведено приклади та описи можливих станів сутностей та правил їх переходів. Досліджено перспективи застосування теорії графів для вирішення поставленої у статті проблеми. На підставі проведеного дослідження спроектовано архітектуру та реалізовано згідно з нею систему, що складається з мобільного та браузерного (веб-сайт та розширення веб-переглядача Google Chrome) клієнтів. Ціль системи – забезпечити проектні команди легким для освоєння засобом для збирання та оброблення різноманітних відгуків безпосередніх користувачів та зацікавлених сторін. Зокрема, розроблена система дає змогу створювати шаблони відгуків із різними наборами полів та різним типом кожного із них. Результати дослідження застосовано для реалізації функціональності зберігання та опрацювання динамічних станів сутності відгуку в межах розробленої програмної системи. Обґрунтовано вибір інтерфейсного рішення для представлення правил переходів між станами сутності для безпосередніх користувачів. Досліджено та застосовано алгоритм перевірки коректності завдання станів та правил їх переходів.

Finding strongly connected components of simple digraphs based on granulation strategy

Strongly connected components (SCCs) are an important kind of subgraphs in digraphs. It can be viewed as a kind of knowledge in the viewpoint of knowledge discovery. In our previous work, a knowledge discovery algorithm called RSCC was proposed for finding SCCs of simple digraphs based on two operators, k-step R-related set and k-step upper approximation, of rough set theory (RST). RSCC algorithm can find SCCs more efficiently than Tarjan algorithm of linear complexity. However, on the one hand, as the theoretical basis of RST applied to SCCs discovery of digraphs, the theoretical relationships between RST and graph theory investigated in previous work only include four equivalences between fundamental RST and graph concepts relating to SCCs. The reasonability of using the two RST operators to find SCCs still need to be investigated. On the other hand, it is found that there are three SCCs correlations between vertices after we use three RST concepts, R-related set, lower and upper approximation sets, to analyze SCCs. RSCC algorithm ignores these SCCs correlations so that the efficiency of RSCC is affected negatively. For the above two issues, firstly, we explore the equivalence between the two RST operators and Breadth-First Search (BFS) which is one of the most basic graph search algorithms and the most direct way to find SCCs. These equivalences explain the reasonability of using the two RST operators to find SCCs, and enrich the content of the theoretical relationships between RST and graph theory. Secondly, we design a granulation strategy according to these three SCCs correlations. Then an algorithm called GRSCC for finding SCCs of simple digraphs based on granulation strategy is proposed. Experimental results show that GRSCC provides better performance to RSCC.

Further Results on the Controllability of Boolean Control Networks

This note presents further results based on the recent paper [J. Liang, H. Chen, and J. Lam, “An improved criterion for controllability of Boolean control networks,” IEEE Trans. Autom. Control , vol. 62, no. 11, pp. 6012–6018, Nov. 2017]. After some optimizations, the conventional method can be more efficient than the method used in the above paper. We also propose an improved method via combining the well known Tarjan's algorithm and depth-first search technique for the controllability analysis of Boolean control networks (BCNs). As a result, the computational complexity will not exceed $O(N^2)$ with $N=2^n$ , where $n$ is the number of state-variables in a BCN.

Finding strongly connected components of simple digraphs based on generalized rough sets theory

Rough sets theory is not good at discovering knowledge from digraphs which is a kind of relational data. In order to solve this problem, we introduce binary relations derived from simple digraphs and propose a new concept of k-step R-related set in the framework of generalized rough sets theory. In addition, we first investigate the relationships between generalized rough sets theory and graph theory on the basis of mutual representation between binary relations and digraphs. The relationships established in this work make it possible to use generalized rough sets theory to find strongly connected components of simple directed graphs, which previously can be solved only by graph algorithms. An algorithm is correspondingly developed based on the above works, especially k-step R-related set. A series of experiments are carried out to test the proposed algorithm. The results show that our algorithm provides comparable performance to the classical Tarjan algorithm. In addition, the proposed algorithm can be implemented in parallel. And its parallel performance is comparable to existing state-of-the-art parallel algorithms.

Multi-core on-the-fly SCC decomposition

The main advantages of Tarjan's strongly connected component (SCC) algorithm are its linear time complexity and ability to return SCCs on-the-fly, while traversing or even generating the graph. Until now, most parallel SCC algorithms sacrifice both: they run in quadratic worst-case time and/or require the full graph in advance. The current paper presents a novel parallel, on-the-fly SCC algorithm. It preserves the linear-time property by letting workers explore the graph randomly while carefully communicating partially completed SCCs. We prove that this strategy is correct. For efficiently communicating partial SCCs, we develop a concurrent, iterable disjoint set structure (combining the union-find data structure with a cyclic list). We demonstrate scalability on a 64-core machine using 75 real-world graphs (from model checking and explicit data graphs), synthetic graphs (combinations of trees, cycles and linear graphs), and random graphs. Previous work did not show speedups for graphs containing a large SCC. We observe that our parallel algorithm is typically 10-30× faster compared to Tarjan's algorithm for graphs containing a large SCC. Comparable performance (with respect to the current state-of-the-art) is obtained for graphs containing many small SCCs.

A space-efficient algorithm for finding strongly connected components

Tarjan's algorithm for finding the strongly connected components of a directed graph is widely used and acclaimed. His original algorithm required at most v(2+5w) bits of storage, where w is the machine's word size, whilst Nuutila and Soisalon-Soininen reduced this to v(1+4w). Many real world applications routinely operate on very large graphs where the storage requirements of such algorithms is a concern. We present a novel improvement on Tarjan's algorithm which reduces the space requirements to v(1+3w) bits in the worst case. Furthermore, our algorithm has been independently integrated into the widely-used SciPy library for scientific computing.

Concurrent depth-first search algorithms based on Tarjan’s Algorithm

We present concurrent algorithms, based on depth-first search, for three problems relevant to model checking: given a state graph, to find its strongly connected components, which states are in loops, and which states are in "lassos". Each algorithm is a variant of Tarjan's Algorithm. Our algorithms typically exhibit a three- or four-fold speed-up over the corresponding sequential algorithms on an eight-core machine.

Efficient decomposition of strongly connected components on GPUs

The GPU (Graphics Processing Unit) has recently become one of the most power efficient processors in embedded and many other environments, and has been integrated into more and more SoCs (System on Chip). Thus modern GPUs play a very important role in power aware computing. Strongly Connected Component (SCC) decomposition is a fundamental graph algorithm which has wide applications in model checking, electronic design automation, social network analysis and other fields. GPUs have been shown to have great potential in accelerating many types of computations including graph algorithms. Recent work have demonstrated the plausibility of GPU SCC decomposition, but the implementation is inefficient due to insufficient consideration of the distinguishing GPU programming model, which leads to poor performance on irregular and sparse graphs. This paper presents a new GPU SCC decomposition algorithm that focuses on full utilization of the contemporary embedded and desktop GPU architecture. In particular, a subgraph numbering scheme is proposed to facilitate the safe and efficient management of the subgraph IDs and to serve as the basis of efficient source selection. Furthermore, we adopt a multi-source partition procedure that greatly reduces the recursion depth and use a vertex labeling approach that can highly optimize the GPU memory access. The evaluation results show that the proposed approach achieves up to 41x speedup over Tarjan's algorithm, one of the most efficient sequential SCC decomposition algorithms, and up to 3.8x speedup over the previous GPU algorithms.

Generating Integration Test Orders for Aspect Oriented Software with Multi-objective Algorithms

The problem known as CAITO refers to the determination of an order to integrate and test classes and aspects that minimizes stubbing costs. Such problem is NP-hard and to solve it efficiently, search based algorithms have been used, mainly evolutionary ones. However, the problem is very complex since it involves different factors that may influence the stubbing process, such as complexity measures, contractual issues and so on. These factors are usually in conflict and different possible solutions for the problem exist. To deal properly with this problem, this work explores the use of multi-objective optimization algorithms. The paper presents results from the application of two evolutionary algorithms - NSGA-II and SPEA2 - to the CAITO problem in four real systems, implemented in AspectJ. Both multi-objective algorithms are evaluated and compared with the traditional Tarjan's algorithm and with a mono-objective genetic algorithm. Moreover, it is shown how the tester can use the found solutions, according to the test goals.