Maximum Matching Algorithm Research Articles

A greedy approach for carpool scheduling optimisation in smart cities

ABSTRACT Nowadays, large cities face numerous problems caused by the rapidly increasing number of vehicles on road. Carpooling has been shown as an efficient solution to ease the traffic pressure. The objective of our carpool scheduling problem is to minimise the number of carpools needed to transport users. Previous research on the similar topic introduces static capacity constraint which limits the carpool size to the vehicle's capacity. However, it is unnecessary since a seat in the vehicle can be occupied by several passengers if their routes are not overlapped. In this paper, we remove this constraint, which allows a vehicle to serve more users than its capacity. We propose a greedy approach based on the iterative matching and merging. Specifically, starting from a set of single-user carpools, the algorithm iteratively checks the merge-ability between carpools, and then applies the maximum matching algorithm to maximise the number of carpools merged. In addition, two methods are proposed to reduce the time complexity of merge-ability checking process. Furthermore, we improve the time efficiency of our algorithms by exploiting geometry properties. Experimental results on synthetic and real-world datasets show that our algorithms have better performances than baseline.

On extensions of the deterministic online model for bipartite matching and max-sat

The surprising results of Karp, Vazirani and Vazirani [39] and (respectively) Buchbinder et al. [18] are examples where rather simple randomization provides provably better approximations than the corresponding deterministic counterparts for online bipartite matching and (respectively) unconstrained non-monotone submodular. We show that seemingly strong extensions of the deterministic online computation model can at best match the performance of naive randomization. More specifically, for bipartite matching, we show that in the priority model (allowing very general ways to order the input stream), we cannot improve upon the trivial 12 approximation achieved by any greedy maximal matching algorithm and likewise cannot improve upon this approximation by any lognlog⁡log⁡n number of online algorithms running in parallel. The latter result yields an improved log⁡log⁡n−log⁡log⁡log⁡n lower bound for the number of advice bits needed to beat the simple deterministic greedy algorithm. For max-sat, we adapt the recent de-randomization approach of Buchbinder and Feldman [16] applied to the Buchbinder et al. [17] algorithm for max-sat to obtain a deterministic 34 approximation algorithm using width 2n parallelism. In order to improve upon this approximation, we show that exponential width parallelism of online algorithms is necessary (in a model that is more general than what is needed for the width 2n algorithm). We relate our results to previous work concerning the priority Branching Tree (pBT) model of Alekhnovich et al. [2].

Studying the benefits of carpooling in an urban area using automatic vehicle identification data

Carpooling has been considered a solution for alleviating traffic congestion and reducing air pollution in cities. However, the quantification of the benefits of large-scale carpooling in urban areas remains a challenge due to insufficient travel trajectory data. In this study, a trajectory reconstruction method is proposed to capture vehicle trajectories based on citywide license plate recognition (LPR) data. Then, the prospects of large-scale carpooling in an urban area under two scenarios, namely, all vehicle travel demands under real-time carpooling condition and commuter vehicle travel demands under long-term carpooling condition, are evaluated by solving an integer programming model based on an updated longest common subsequence (LCS) algorithm. A maximum weight non-bipartite matching algorithm is introduced to find the optimal solution for the proposed model. Finally, road network trip volume reduction and travel speed improvement are estimated to measure the traffic benefits attributed to carpooling. This study is applied to a dataset that contains millions of LPR data recorded in Langfang, China for 1 week. Results demonstrate that under the real-time carpooling condition, the total trip volumes for different carpooling comfort levels decrease by 32–49%, and the peak-hour travel speeds on most road segments increase by 5–40%. The long-term carpooling relationship among commuter vehicles can reduce commuter trips by an average of 30% and 24% in the morning and evening peak hours, respectively, during workdays. This study shows the application potential and promotes the development of this vehicle travel mode.

RETRACTED ARTICLE: Research and Experiment of Intelligent Natural Language Processing Algorithms

Natural language processing is mainly divided into two parts: speech processing and word processing. The level of word processing is mainly studied. Natural language processing is divided into lexical analysis, syntax analysis and semantic analysis. Aiming at the scope of the language ambiguity and thesaurus in the field of smart home, the maximal matching algorithm is used to segment the natural language. Then, through the way of template matching, semantic comprehension finally forms the code form that can control the home node. In the system applied in this paper, the speech is processed into words through the existing voice input function of the mobile terminal. Then, the control instruction is obtained through the language processing method. The processed data is communicated to the server via socket. The server sends the data to the home node through the Zigbee protocol. Finally, control of home appliances is achieved.

Maximum match filtering algorithm to defend spectrum-sensing data falsification attack in CWSN

Cognitive Wireless Sensor Networks (CWSNs) provide better bandwidth utilisation compared to normal Wireless Sensor Networks (WSNs) by using opportunistic spectrum access to transfer data. They transmit data through the primary user's spectrum band when there is heavy traffic in its own network, thereby eliminating collisions and delays in data delivery. During this, CWSNs are subject to several security threats, attacks on secrecy and authentication, attacks on network availability (DOS attacks), stealth attacks on service integrity etc. The Spectrum Sensing Data Falsification (SSDF) attack is a type of DOS attack where the attackers modify the spectrum sensing report to compel the base station to take a wrong collaborative decision regarding the vacant spectrum band in other networks. In this paper, we have proposed the Maximum-Match Filtering algorithm (MMF) for collaborative spectrum sensing and spectrum decision making in CWSNs, which is executed at the base station to counter the SSDF attack.

An o(n<sup>2.5</sup>) Algorithm: For Maximum Matchings in General Graphs

This article extend the John E. Hopcroft and Richart M. Karp Algorithm (HK Algorithm) for maximum matchings in bipartite graphs to the non-bipartite case by providing a new approach to deal with the blossom in alternating paths in the process of searching for augmenting paths, which different from well-known “shrinking” way of Edmonds and makes the algorithm for maximum matchings in general graphs more simple.

Алгоритм сегментації слів на основі пошуку найкоротшого шляху в графі

The features of word segmentation algorithms from such texts are considered. There are two main models, namely, statistical one and the one using a dictionary. For models with a dictionary, a variant of the maximal matching algorithm is noted for which there are modifications such as Forward Maximal Matching (FMM) and Backward Maximal Matching (BMM) to be depending on the direction of text processing. The second option for models with a dictionary is an algorithm that finds segmentation with a minimum number of words. A new algorithm for words segmenting based on a modified wave algorithm has been presented. The algorithm takes into account the features of the input data and is built in such a way that the necessary calculations are performed in a single pass. This reduces its computational complexity. A description of the word segmentation algorithm is given. An example is shown of splitting an input string in English into words, representing it in the form of a graph and finding the shortest path.To assess the quality of segmentation, the EDWS (Edit Distance of the Word Separator) method is presented. A special tool was used to assess the segmentation of Chinese words with a test corpora based on news texts. Evaluations of the quality of segmentation of words for the proposed algorithm (based on the search for the shortest path) and a number of other known segmentators are obtained. An example of segmentation of a news text in Russian is given. The possibilities of using the developed algorithm in the problems of information search in national resources of the Internet are shown. The implementation of the word segmentation algorithm is used when creating a generalized domain model based on monitoring of the Chinese Internet segment resources.The increase in the number of information resources of the Chinese Internet segment makes it necessary to create of global information retrieval systems. For search indexes of such systems, fast, accurate and complete segmentation of words from texts is necessary. The obtained estimates of segmentation quality using the proposed algorithm for the formation of the search system index indicate the possibility of its use for information resources of the Chinese Internet-segment.

An artificial immune network to control interrupted flow at a signalized intersection

To monitor and control interrupted flow at signalized intersections, several Traffic Signal Control Systems (TSCSs) were developed based on optimization and artificial intelligence techniques. Although learning can provide intelligent ways to deal with disturbances, existing approaches still lack concepts and mechanisms that enable direct representation of knowledge and explicit learning, particularly to capture and reuse previous experiences with disturbances. This article addresses this gap by designing a new TSCS based on innovative concepts and mechanisms borrowed from biological immunity. Immune memory enables the design of a Case-Based Reasoning (CBR) System in which cases provide a direct representation of knowledge about disturbances. Immune network theory enables the design of a Reinforcement Learning (RL) mechanism to interconnect cases, capture explicit knowledge about the outcomes (success and failure) of control decisions and enable decision-making by taking advantage of previous outcomes in reaction to new occurrences of disturbances. We provide a detailed description of new learning algorithms, both to create the case-base and to interconnect cases using RL. The performance of the suggested TSCS is assessed by benchmarking it against two standard control strategies from the literature, namely fixed-time and adaptive control using the Longest Queue First – Maximal Weight Matching (LQF-MWM) algorithm. The suggested TSCS is applied on an intersection simulated using VISSIM, a state-of-the-art traffic simulation software. The results show that the suggested TSCS is able to handle different traffic scenarios with competitive performance, and that it is recommended for extreme situations involving blocked approaches and high traffic flow.

Optimality of Fast-Matching Algorithms for Random Networks With Applications to Structural Controllability

Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There are many notions of controllability, one of them being structural controllability , which is intimately connected to finding maximum matchings on the underlying network topology. In this work, we study fast, scalable algorithms for finding maximum matchings for a large class of random networks . First, we illustrate that degree distribution random networks are realistic models for real networks in terms of structural controllability. Subsequently, we analyze a popular, fast, and practical heuristic due to Karp and Sipser as well as a simplification of it. For both heuristics, we establish asymptotic optimality and provide results concerning the asymptotic size of maximum matchings for an extensive class of random networks.

An efficient algorithm for finding all possible input nodes for controlling complex networks

Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. Finding an MIS is known to be equivalent to computing a maximum matching of the network, where the unmatched nodes constitute an MIS. However, maximum matching is often not unique for a network, and finding all possible input nodes, the union of all MISs, may provide deep insights to the controllability of the network. Here we present an efficient enumerative algorithm for the problem. The main idea is to modify a maximum matching algorithm to make it efficient for finding all possible input nodes by computing only one MIS. The algorithm can also output a set of substituting nodes for each input node in the MIS, so that any node in the set can replace the latter. We rigorously proved the correctness of the new algorithm and evaluated its performance on synthetic and large real networks. The experimental results showed that the new algorithm ran several orders of magnitude faster than an existing method on large real networks.

The Weighted Matching Approach to Maximum Cardinality Matching

Several papers have achieved time $O(\sqrt n m)$ for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds' algorithm to derive the structure of shortest augmenting paths. We extend this to a complete algorithm for maximum cardinality matching in time $O(\sqrt n m)$.

Multi-agent immune networks to control interrupted flow at signalized intersections

Urban traffic is subject to disturbances that cause long queues and extended waiting times at signalized intersections. Although Multi-Agent Systems (MAS) were considered to control traffic at signalized intersections in a distributed way, their generic conceptual framework and lack of built-in adaptation mechanisms prevent them from achieving specific disturbance management capabilities. The traffic signal control problem is still a challenging open-ended problem for which learning and adaptation mechanisms need to be developed to deal with disturbances in an intelligent way. In this article, we rely on concepts and mechanisms inspired by biological immunity to design a distributed, intelligent and adaptive traffic signal control system. We suggest a heterarchical multi-agent architecture, where each agent represents a traffic signal controller assigned to a signalized intersection. Each agent communicates and coordinates with neighboring agents, and achieves learning and adaptation to disturbances based on an artificial immune network. The suggested Immune Network Algorithm based Multi-Agent System (INAMAS) provides intelligent mechanisms that capture disturbance-related knowledge explicitly and take advantage of previous successes and failures in dealing with disturbances through an adaptation of the reinforcement principle. To demonstrate the efficiency of the suggested control architecture, we assess its performance against two control strategies from literature, namely fixed-time control and a distributed adaptation of the Longest Queue First – Maximal Weight Matching (LQF-MWM) algorithm. Agents are developed using SPADE platform and used to control a network of signalized intersections simulated with VISSIM, a state-of-the-art traffic simulation software. The results show that INAMAS is able to handle different traffic scenarios with competitive performance (in terms of vehicle queue lengths and waiting times), and that it is particularly more successful than the other controllers in dealing with extreme situations involving blocked approaches and high traffic volumes.

Maximum linear matching: Intelligent and automatic wavelength calibration method

SummaryWavelength calibration is a necessary means to ensure the normal operation of the spectrometer. In general, calibration light sources that can emit fixed wavelength (such as mercury‐argon lamp) are utilized to generate spectral line on the linear array charge‐coupled device detector. Thus, it is a prerequisite for wavelength calibration to match the pixel position of the well‐divided spectral line with light of different wavelength emitted by calibration light source correctly. In this paper, we aim to present a method to make calibration procedure intelligent and automatic by machine. We establish a pixel‐wavelength model based on bipartite graph and propose the maximum linear matching (MLM) algorithm to find the correct set of pixel‐wavelength automatically. Meanwhile, we calculate precision and recall to measure the effectiveness of MLM and analyze the practical application of MLM by comparing it with conventional artificial methods. Experiments show that the autocalibration method based on MLM can calibrate many types of grating spectrometer more accurately and more reliably. With MLM, we report 98.33% precision and 94.59% recall on 8 groups of experiments.

A Weighted Maximum Matching Algorithm for Influence Maximization and Structural Controllability

Structural control and influence maximization on networks both admit the problem of selecting a particular subset of nodes. In structural control, the subset of nodes should guarantee the controllability of the network (in the usual sense) for almost any combination of weights. In influence maximization, given a diffusion process over the network, the chosen subset of nodes (of a given cardinality) should produce the greatest diffusive influence over the rest of the network. While structural control exploits only the structure of the network, influence maximization depends both on the structure and the weights of the edges. We modify an algorithm originally developed for structural control to take advantage of the weights as well, and we show it can be used to find competitive solutions to the influence maximization problem, while guaranteeing structural controllability. This also suggests an underlying similarity between these models, despite their intrinsic differences and the contexts in which they are usually used. We develop analytic results for two extreme cases, the binary tree and the two-level star graph, as well as empirical results for a selection of random graphs.

An optimized DNA based encryption scheme with enforced secure key distribution

More and more sensitive information is transmitted and stored in computer networks. Security has become a critical issue. As traditional cryptographic systems are now vulnerable to attacks, DNA based cryptography has been identified as a promising technology because of the vast parallelism and extraordinary information density. While a body of research has proposed the DNA based encryption algorithm, no research has provided solutions to distribute complex and long secure keys. This paper introduces a Hamming code and a block cipher mechanism to ensure secure transmission of a secure key. The research overcomes the limitation on the length of the secure key represented by DNA strands. Therefore it proves that real biological DNA strands are useful for encryption computing. To evaluate our method, we apply the block cipher mechanism to optimize a DNA-based implementation of a conventional symmetric encryption algorithm, described as “yet another encryption algorithm”. Moreover, a maximum length matching algorithm is developed to provide immunity against frequency attacks.

Efficient maximum matching algorithms for trapezoid graphs

Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NP-hard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an $O(n(\log n)^3)$ algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to $O(n(\log n)^2)$. Finally, we generalize this algorithm to a larger graph class, namely $k$-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.

Identification of critical regulatory genes in cancer signaling network using controllability analysis

Cancer is characterized by a complex web of regulatory mechanisms which makes it difficult to identify features that are central to its control. Molecular integrative models of cancer, generated with the help of data from experimental assays, facilitate use of control theory to probe for ways of controlling the state of such a complex dynamic network. We modeled the human cancer signaling network as a directed graph and analyzed it for its controllability, identification of driver nodes and their characterization. We identified the driver nodes using the maximum matching algorithm and classified them as backbone, peripheral and ordinary based on their role in regulatory interactions and control of the network. We found that the backbone driver nodes were key to driving the regulatory network into cancer phenotype (via mutations) as well as for steering into healthy phenotype (as drug targets). This implies that while backbone genes could lead to cancer by virtue of mutations, they are also therapeutic targets of cancer. Further, based on their impact on the size of the set of driver nodes, genes were characterized as indispensable, dispensable and neutral. Indispensable nodes within backbone of the network emerged as central to regulatory mechanisms of control of cancer. In addition to probing the cancer signaling network from the perspective of control, our findings suggest that indispensable backbone driver nodes could be potentially leveraged as therapeutic targets. This study also illustrates the application of structural controllability for studying the mechanisms underlying the regulation of complex diseases.

Fully-Dynamic Graph Algorithms with Sublinear Time Inspired by Distributed Computing

We study dynamic graphs in the fully-dynamic centralized setting. In this setting the vertex set of size n of a graph G is fixed, and the edge set changes step-by-step, such that each step either adds or removes an edge. The goal in this setting is maintaining a solution to a certain problem (e.g., maximal matching, edge coloring) after each step, such that each step is executed efficiently. The running time of a step is called update-time. One can think of this setting as a dynamic network that is monitored by a central processor that is responsible for maintaining the solution. Currently, for several central problems, the best-known deterministic algorithms for general graphs are the naive ones which have update-time O(n). This is the case for maximal matching and proper O(∆)-edge-coloring. The question of existence of sublinear in n update-time deterministic algorithms for dense graphs and general graphs remained wide open. We address this question by devising sublinear update-time deterministic algorithms for maximal matching in graphs with bounded neighborhood independence o(n/ log2 n), and for proper O(∆)-edge-coloring in general graphs. The family of bounded neighborhood independence is a very wide family of dense graphs that represent very well various networks. For graphs with constant neighborhood independence, our maximal matching algorithm has Õ(√n) update-time. Our O(∆)-edge-coloring algorithms has Õ(√∆) update-time for general graphs.In order to obtain our results we employ a novel approach that adapts certain distributed algorithms of the LOCAL setting to the centralized fully-dynamic setting. This is achieved by optimizing the work each processors performs, and efficiently simulating a distributed algorithm in a centralized setting. The simulation is efficient thanks to a careful selection of the network parts that the algorithm is invoked on, and by deducing the solution from the additional information that is present in the centralized setting, but not in the distributed one. Our experiments on various network topologies and scenarios demonstrate that our algorithms are highly-efficient in practice. We believe that our approach is of independent interest and may be applicable to additional problems.

A Self-Stabilizing Algorithm for Maximal Matching in Anonymous Networks

We propose a self-stabilizing algorithm for computing a maximal matching in an anonymous network. The complexity is O(2) moves with high probability, under the adversarial distributed daemon. Among all adversarial distributed daemons and with the anonymous assumption, our algorithm provides the best known complexity. Moreover, the previous best known algorithm working under the same daemon and using identity has a O(m) complexity leading to the same order of growth than our anonymous algorithm. Finally, we do not make the common assumption that a node can determine whether one of its neighbors points to it or to another node, and still we present a solution with the same asymptotic behavior.

Randomized OBDD-based graph algorithms

Implicit graph algorithms deal with the characteristic function χE of the edge set E of a graph G=(V,E). Encoding the nodes by binary vectors, χE can be represented by an Ordered Binary Decision Diagram (OBDD) which is a well known data structure for Boolean functions. OBDD-based graph algorithms solve graph optimization problems by mainly using functional operations and are a heuristic approach to cope with massive graphs. These algorithms heavily rely on a compact representation of the underlying Boolean functions which is why all previously known OBDD-based algorithms are deterministic since random functions are not compressible in general. Here, the first randomized OBDD-based algorithms are presented where random functions with limited independence are used to overcome the large representation size. On the theoretical part, we investigate the size of OBDDs representing k-wise independent random functions. In addition, we give a construction of almost k-wise independent random functions by means of a random OBDD generation and show an almost matching lower bound of the OBDD size representing such random functions. On the algorithmic part, randomization often facilitates the design of simple algorithms which in the context of OBDD-based algorithms means a small number of functional operations and as few input variables of the used Boolean functions as possible. We present two randomized implicit algorithms: A randomized minimum spanning tree algorithm and a maximal matching algorithm. The matching algorithm needs O(log3⁡|V|) functional operations in expectation and uses functions with at most 3log⁡|V| variables which is both better than the best known deterministic algorithms w.r.t. functional operations and variables. The algorithm may be of independent interest. The experimental evaluation of the algorithms shows that they outperform known OBDD-based algorithms for the maximal matching problem and the minimum spanning tree problem.