Depth First Search Approach Research Articles

A depth-first search approach to detect the community structure of weighted networks using the neighbourhood proximity measure

A depth-first search approach to detect the community structure of weighted networks using the neighbourhood proximity measure

An Effective Two-Stage Algorithm for the Bid Generation Problem in the Transportation Service Market

This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm’s efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions.

Multi-Path Routing Algorithm Based on Deep Reinforcement Learning for SDN

Software-Defined Networking (SDN) enhances network control but faces Distributed Denial of Service (DDoS) attacks due to centralized control and flow-table constraints in network devices. To overcome this limitation, we introduce a multi-path routing algorithm for SDN called Trust-Based Proximal Policy Optimization (TBPPO). TBPPO incorporates a Kullback–Leibler divergence (KL divergence) trust value and a node diversity mechanism as the security assessment criterion, aiming to mitigate issues such as network fluctuations, low robustness, and congestion, with a particular emphasis on countering DDoS attacks. To avoid routing loops, differently from conventional ‘Next Hop’ routing decision methodology, we implemented an enhanced Depth-First Search (DFS) approach involving the pre-computation of path sets, from which we select the best path. To optimize the routing efficiency, we introduced an improved Proximal Policy Optimization (PPO) algorithm based on deep reinforcement learning. This enhanced PPO algorithm focuses on optimizing multi-path routing, considering security, network delay, and variations in multi-path delays. The TBPPO outperforms traditional methods in the Germany-50 evaluation, reducing average delay by 20%, cutting delay variation by 50%, and leading in trust value by 0.5, improving security and routing efficiency in SDN. TBPPO provides a practical and effective solution to enhance SDN security and routing efficiency.

Blocking Trails for f-factors of Multigraphs

Blocking flows were introduced by Dinic (Soviet Math Doklady 11: 1277–1280, 1970) to speed up the computation of maximum network flows. They have been used in algorithms for problems such as maximum cardinality matching of bipartite graphs Hopcroft and Karp (SIAM J Comput 2(4), 225–231, 1973) and general graphs Micali and Vazirani (in: Proceedings of the 21st Annual Symposium on Foundations of Computer Science, 17–27, 1980), maximum weight matching of general graphs Gabow and Tarjan (J ACM 38(4), 815–853, 1991), and many others. The blocking algorithm of Gabow and Tarjan (1991) for matching is based on depth-first search. We extend the depth-first search approach to find f-factors of general multigraphs. Here f is an arbitrary integral-valued function on vertices, an f-matching is a subgraph where every vertex x has degree $$\le f(x)$$ , an f-factor has equality in every degree bound. A set of blocking trails for an f-matching M is a maximal collection $$\mathcal{A}$$ of edge-disjoint augmenting trails such that $$M\bigoplus _{A\in {\mathcal{A}}} A $$ is a valid f-matching. Blocking trails are needed in efficient algorithms for maximum cardinality f-matching Huang and Pettie (Algorithmica 84(7): 1952–1992, 2022), maximum weight f-factors/matchings by scaling Duan et al. (In: Proceedings of the 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Vol. 168 of LIPIcs, 41:1-41:17, 2020; Gabow (A weight-scaling algorithm for f-factors of multigraphs. arXiv:2010.01102 , 2020), and approximate maximum weight f-factors and f-edge covers Huang and Pettie (2022). Since these algorithms find many sets of blocking trails, the time to find blocking trails is a dominant factor in the running time. Our blocking trail algorithm runs in linear time O(m). In independent work and using a different approach, Huang and Pettie (2022) present a blocking trails algorithm using time $$O(m\alpha (m,n))$$ . As examples of the time bounds for the above applications, an approximate maximum weight f-factor is found in time $$O(m\,\alpha (m,n))$$ using Huang and Pettie (2022), and our algorithm eliminates the factor $$\alpha (m,n)$$ . Similarly a maximum weight f-factor is found in time $$O(\sqrt{\Phi \log \Phi }\, m\,\alpha (m,n)\, \log (\Phi W))\,$$ using Huang and Pettie (2022) , ( $$\Phi =\sum _{v\in V} f(v)$$ , W the maximum edge weight) and our algorithm eliminates the $$\alpha (m,n)$$ factor, making the time within a factor $$\sqrt{\log {\Phi }}$$ of the bound for bipartite multigraphs. The technical difficulty for this work stems from the fact that a fixed vertex can occur many times in a given search. This does not occur in ordinary matching or in algorithms for maximum cardinality or maximum weight f-matching. These multiple occurrences can create a new variant of blossom, the “skew blossom”. Also they can make blossoms become “incomplete”, i.e., partially processed yet still relevant in future searches.

Fast and optimal branch-and-bound planner for the grid-based coverage path planning problem based on an admissible heuristic function.

This paper introduces an optimal algorithm for solving the discrete grid-based coverage path planning (CPP) problem. This problem consists in finding a path that covers a given region completely. First, we propose a CPP-solving baseline algorithm based on the iterative deepening depth-first search (ID-DFS) approach. Then, we introduce two branch-and-bound strategies (Loop detection and an Admissible heuristic function) to improve the results of our baseline algorithm. We evaluate the performance of our planner using six types of benchmark grids considered in this study: Coast-like, Random links, Random walk, Simple-shapes, Labyrinth and Wide-Labyrinth grids. We are first to consider these types of grids in the context of CPP. All of them find their practical applications in real-world CPP problems from a variety of fields. The obtained results suggest that the proposed branch-and-bound algorithm solves the problem optimally (i.e., the exact solution is found in each case) orders of magnitude faster than an exhaustive search CPP planner. To the best of our knowledge, no general CPP-solving exact algorithms, apart from an exhaustive search planner, have been proposed in the literature.

Information Set Generation in Partially Observable Games

We address the problem of making single-point decisions in large partially observable games, where players interleave observation, deliberation, and action. We present information set generation as a key operation needed to reason about games in this way. We show how this operation can be used to implement an existing decision-making algorithm. We develop a constraint satisfaction algorithm for performing information set generation and show that it scales better than the existing depth-first search approach on multiple non-trivial games.

Low‐complexity block tree image coder for visual sensor networks

The wavelet block tree coding (WBTC) algorithm is an efficient wavelet-based image coder. In this coder, multiple spatial orientation trees are combined together to make a single block tree. It uses three ordered lists to keep track of significant/insignificant coefficients and sets while coding, which increases its memory requirement as well as computational complexity. Also, it uses memory inefficient conventional discrete wavelet transform (DWT) to compute the transformed coefficients. In this study, a Low-Complexity Block Tree Coding (LCBTC) algorithm that uses two state-tables and two very small lists, is proposed. Similar to WBTC, it also uses sorting and refinement passes in each bit-plane. However, it encodes the coefficients in block-tree manner using depth-first search approach to reduce the computational complexity. It uses DWT coefficients obtained from modified fractional wavelet filter (MFrWF) rather than conventional DWT, which further reduces the overall memory and complexity of the image coder. The simulation results show that the memory requirement and computational complexity of LCBTC is much less than WBTC and other state-of-the-art coding algorithms. These features make the image coder a better candidate for compression in memory constrained and real-time visual sensor networks.

Depth-first Search Approach for Language-based Opacity Verification Using Petri Nets

Abstract The rapidly growing use of modern computer-integrated systems involving critical assets underscores the need for developing measures to guarantee their security against malicious attacks. This paper deals with the problem of language-based opacity formulation and verification in the framework of discrete event systems modeled with partially observed Petri nets (POPNs). In this context, a secret behavior is defined as a sub-language that should be hidden from an intruder who partially observes the system’s evolution. A Petri net system is qualified as language opaque if no observation leads to an event sequence estimation that is entirely contained in a secret. In this paper, we develop a depth-first search algorithm that verifies the language opacity of a POPN system. More specifically, the proposed algorithm checks the existence of a non-secret transition sequence that is observably equivalent to a secret one by performing a depth-first search on a portion of the system’s execution. Complexity analysis and experimental results are presented to illustrate the efficiency of the proposed approach.

Graph Mining Using gSpan: Graph-Based Substructure Pattern Mining

We have explored new methodologies for regular graph-based pattern exploration in graph datasets and studied a novel algorithm called gSpan (graph-based substructure pattern mining), which finds frequent substructures without candidate production. gSpan fabricates another lexicographic arrangement between diagrams and maps every chart to a kind smaller depth-first search (DFS) code as its standard label. Taking into account this lexico- realistic request, gSpan embraces the depth-First search approach to mine regular associated subgraphs efficiently. Our performance study demonstrates that gSpan significantly beats previous calculations, once in a while by a request of scale.

A Depth-First Search Approach for Mining Proportional Fault-Tolerant Frequent Patterns Efficiently in Large Database

A Depth-First Search Approach for Mining Proportional Fault-Tolerant Frequent Patterns Efficiently in Large Database

Energy efficient online routing of flows with additive constraints

A number of studies report that ICT sectors are responsible for up to 10% of the worldwide power consumption and that a substantial share of such amount is due to the Internet infrastructure. To accommodate the traffic in the peak hours, Internet Service Providers (ISP) have overprovisioned their networks, with the result that most of the links and devices are under-utilized most of the time. Thus, under-utilized links and devices may be put in a sleep state in order to save power and that might be achieved by properly routing traffic flows. In this paper, we address the design of a joint admission control and routing scheme aiming at maximizing the number of admitted flow requests while minimizing the number of nodes and links that need to stay active. We assume an online routing paradigm, where flow requests are processed one-by-one, with no knowledge of future flow requests. Each flow request has requirements in terms of bandwidth and m additive measures (e.g., delay, jitter). We develop a new routing algorithm, E2-MCRA, which searches for a feasible path for a given flow request that requires the least number of nodes and links to be turned on. The basic concepts of E2-MCRA are look-ahead, the depth-first search approach and a path length definition as a function of the available bandwidth, the additive QoS constraints and the current status (on/off) of the nodes and links along the path. Finally, we present the results of the simulation studies we conducted to evaluate the performance of the proposed algorithm.

A width-recursive depth-first tree search approach for the design of discrete coefficient perfect reconstruction lattice filter bank

The lattice structure two-channel orthogonal filter bank structurally guarantees the perfect reconstruction (PR) property. Thus, it is eminently suitable for hardware realization even under severe coefficient quantization condition. Nevertheless, its frequency response is still adversely affected by coefficient quantization. In this paper, a novel recursive-in-width depth-first tree search technique is presented for the design of lattice structure PR orthogonal filter banks subject to discrete coefficient value constraint. A frequency-response deterioration measure is developed to serve as a branching criterion. At any node, the coefficient which will cause the largest deterioration in the frequency response of the filter when quantized is selected for branching. The improvement in the frequency response ripple magnitude achieved by our algorithm over that by simple rounding of coefficient values differs widely from example to example ranging from a fraction of a decibel to over 10 dB.

Over 20 years of reaction access systems from MDL: a novel reaction substructure search algorithm.

From REACCS, to MDL ISIS/Host Reaction Gateway, and most recently to MDL Relational Chemistry Server, a new product based on Oracle data cartridge technology, MDL's reaction database management and retrieval systems have undergone great changes. The evolution of the system architecture is briefly discussed. The evolution of MDL reaction substructure search (RSS) algorithms is detailed. This article mainly describes a novel RSS algorithm. This algorithm is based on a depth-first search approach and is able to fully and prospectively use reaction specific information, such as reacting center and atom-atom mapping (AAM) information. The new algorithm has been used in the recently released MDL Relational Chemistry Server and allows the user to precisely find reaction instances in databases while minimizing unrelated hits. Finally, the existing and new RSS algorithms are compared with several examples.

Algorithm portfolios

Stochastic algorithms are among the best methods for solving computationally hard search and reasoning problems. The run time of such procedures can vary significantly from instance to instance and, when using different random seeds, on the same instance. One can take advantage of such differences by combining several algorithms into a portfolio, and running them in parallel or interleaving them on a single processor. We provide an evaluation of the portfolio approach on distributions of hard combinatorial search problems. We show under what conditions the portfolio approach can have a dramatic computational advantage over the best traditional methods. In particular, we will see how, in a portfolio setting, it can be advantageous to use a more “risk-seeking” strategy with a high variance in run time, such as a randomized depth-first search approach in mixed integer programming versus the more traditional best-bound approach. We hope these insights will stimulate the development of novel randomized combinatorial search methods.

Multitarget tracking in clutter: fast algorithms for data association

Three fast algorithms have been developed to solve the problem of data association in multitarget tracking in clutter. In the first algorithm, the problem of data association is identified as an exhaustive search problem in general. Subsequently, a mathematical model is proposed for the problem of data association in the joint probabilistic data association filter (JPDAF). Based on the model, a depth-first search (DFS) approach is developed for the fast generation of data association hypotheses and the computation of the conditional probabilities of the hypotheses in the JPDAF. When the density of targets is moderate, a second algorithm is developed to directly compute a posteriori probabilities in the JPDAF without generating the data association hypotheses. In the third algorithm, the effect of interference due to closely spaced targets is simplified. An approach to approximately compute the a posteriori probabilities in the JPDAF is developed. The computational complexity of the algorithms is analyzed in the worst case, as well as in the average case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Depth-first search approach for fault-tolerant routing in hypercube multicomputers

Using depth-first search, the authors develop and analyze the performance of a routing scheme for hypercube multicomputers in the presence of an arbitrary number of faulty components. They derive an exact expression for the probability of routing messages by way of optimal paths (of length equal to the Hamming distance between the corresponding pair of nodes) from the source node to an obstructed node. The obstructed node is defined as the first node encountered by the message that finds no optimal path to the destination node. It is noted that the probability of routing messages over an optimal path between any two nodes is a special case of the present results and can be obtained by replacing the obstructed node with the destination node. Numerical examples are given to illustrate the results, and they show that, in the presence of component failures, depth-first search routing can route a message to its destination by means of an optimal path with a very high probability. >