Searching networks with unrestricted edge costs

In this research work, we present a combination of a memetic algorithm and an immunological algorithm that we call Memetic Immunological Algorithm - MIA. This algorithm has been designed to tackle the resource allocation problem on a communication network. The aim of the problem is to supply all resource requested on a communication network with minimal costs and using a fixed number of providers, everyone with a limited resource quantity to be supplied. The scheduling of several resource allocations is a classical combinatorial problem that finds many applications in real-world problems. MIA incorporates two deterministic approaches: (1) a local search operator, which is based on the exploration of the neighbourhood; and (2) a deterministic approach for the assignment scheme based on the Depth First Search (DFS) algorithm. The results show that the usage of a local search procedure and mainly the DFS algorithm is an effective and efficient approach to better exploring the complex search space of the problem. To evaluate the performances of MIA we have used 28 different instances. The obtained results suggest that MIA is an effective optimization algorithm in terms of the quality of the solution produced and of the computational effort.

Efficient access to timely information is critical in today's digital era. Web crawlers, automated programs that navigate the Internet, play an important role in collecting data from websites such as Kumparan, a leading news site in Indonesia. This research shows the effectiveness of the Breadth-First Search (BFS) and Depth-First Search (DFS) algorithms in indexing Kumparan content. The results of the research show that BFS consistently indexes more files comprehensively but with longer execution times compared to DFS, which provides faster initial results but with fewer files. For example, at depth 4 BFS indexed 949 files in 886.94 seconds, while DFS indexed 470 files in 233.02 seconds. These findings highlight the balance between precision and speed when selecting a crawling algorithm tailored to the needs of a particular website. This research provides insights into optimizing web crawler technology for complex websites such as Coil and suggests avenues for further research to improve permission efficiency and adaptability across a variety of crawling scenarios.

Diverse best-first search (DBFS) is a successful algorithm for satisficing planning that is built on top of greedy best-first search and uses stochastic search techniques to select the next ``best'' state that is not always in agreement with the heuristic function. DBFS thus considers a diversity of search directions and avoids search plateaus caused by inaccurate heuristic estimation. However, the scalability of DBFS is still limited by the available memory resource, as in any planning system that uses best-first search at its core. This paper presents the diverse depth-first search (DDFS) algorithm that overcomes the memory bottleneck of DBFS. DDFS requires much less memory than DBFS yet it successfully incorporates DBFS' randomized node selection scheme for effective search diversification. Additionally, DDFS is enhanced with a transposition table to avoid duplicate search effort commonly found in depth-first search. Experimental results in solving problems used in previous International Planning Competitions show that DDFS can solve instances that remain unsolvable by DBFS due to its excessive memory requirements.

Research on space efficient graph algorithms, particularly for st-connectivity, has a long history including the celebrated polynomial time, O(lg n) bits1 algorithm in undirected graphs by Reingold J. JACM. 55(4) (2008), and polynomial time, \(n/2^{\Theta (\sqrt {\lg n})}\) bits algorithm in directed graphs by Barnes et al. SICOMP. 27(5), 1273–1282 (1998). Recent works by Asano et al. ISAAC (2014) and Elmasry et al. STACS (2015), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of breadth first search (BFS) in a graph G with n vertices and m edges, taking the optimal O(m + n) time using O(n) bits improving the naive O(n lg n) bits implementation. Similarly, Asano et al. provided space efficient implementations for performing depth first search (DFS) in a graph G. We continue this line of work focusing on improving the space requirement for implementing a few classical graph algorithms. Our first result is a simple data structure that can maintain any subset S of a universe of u elements using just u + o(u) bits and supports in constant time, apart from the standard insert, delete and membership queries, the operation findany that finds and returns any element of the set (or outputs that the set is empty). It can also enumerate all elements present currently in the set in no particular order in O(k + 1) time where k is the number of elements currently belonging to the set. While this data structure supports a weaker set of operations than that of Elmasry et al. STACS (2015), it is simple, more space efficient and is sufficient to support a BFS implementation optimally in O(m + n) time using at most 2n + o(n) bits. Later, we further improve the space requirement of BFS to at most n lg 3 + o(n) bits albeit with a slight increase in running time to O(m lg nf(n)) time where f(n) is any extremely slow growing function of n, and the o term in the space is a function of f(n). We also discuss a similar time-space tradeoff result for finding a minimum weight spanning tree of a weighted (bounded by polynomial in n) undirected graph using n + O(n/f(n)) bits and O(m lg nf(n)) time, for any function f(n) such that 1 ≤ f(n) ≤ n. For DFS in a graph G, we provide an implementation taking O(m + n) time and O(n lg m/n) bits. This partially answers at least for sparse graphs, a question asked by Asano et al. ISAAC (2014) whether DFS can be performed in O (m + n) time and using O(n) bits, and also simultaneously improves the DFS result of Elmasry et al. STACS (2015). Using our DFS algorithm and other careful implementations, we show how one can also test for biconnectivity, 2-edge connectivity, and find cut vertices and bridges of a given undirected graph within the same time and space bounds; earlier classical linear time algorithms for these problems used Ω(n lg n) bits of space.

In this paper, we propose a depth-first search (DFS) algorithm for finding maximum matching in general graphs. Unlike blossom shrinking algorithms, which store all possible alternative alternating-paths in the super-vertices shrinking from blossoms, the newly proposed algorithm does not involve blossom shrinking. The basic idea is to deflect the alternating path when facing blossoms. The algorithm maintains detour information in an auxiliary stack to minimize the redundant data structures. A benefit of our technique is to avoid spending the time on shrinking and expanding blossoms. This DFS algorithm can determine a maximum matching of a general graph with m edges and n vertices in 𝑂(𝑚𝑛) time with space complexity 𝑂(𝑛).

In a localized routing algorithm, node A currently holding the message forwards it based on the location of itself, its neighboring nodes and destination. We propose to use depth first search (DFS) method for routing decisions. Each node A, upon receiving the message for the first time, sorts all its neighbors according to a criteria such as their distance to destination and uses that order in DFS algorithm. It is the first localized algorithm that guarantees delivery for (connected) wireless networks modeled by arbitrary graphs, including inaccurate location information. We then propose the first localized QoS routing algorithm for wireless networks. It performs DFS routing algorithm after edges with insufficient bandwidth or insufficient connection time are deleted from the graph, and attempts to minimize hop count. This is also the first paper to apply GPS in QoS routing decisions, and to consider the connection time (estimated lifetime of a link) as a QoS criterion. The average length of measured QoS path in our experiments, obtained by DFS method, was between 1 and 1.34 times longer than the length of QoS path obtained by shortest path algorithm. The overhead is considerably reduced by applying the concept of internal nodes.

Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r1, r2, …, rn, with the ith type having length li, width wi, value vi, and demand constraint bi. It is required to produce, from the stock rectangle S, ai copies of ri, 1 ≤ i ≤ n, to maximize a1v1 + a2v2 + · + anvn subject to the constraints ai ≤ bi. Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.

The subject of the research is one of the ways of updating modern training systems for solving problems of graph theory, namely, automatic generation of graphs. This approach will reduce the load on the training system database and generate tasks for the user in real-time without updating the bank of tasks. In the course of the work, the advantages and disadvantages of this approach were identified. The most suitable method for the implementation of the research was chosen to represent graphs in electronic computers. The requirements for generated graphs and possible ways of implementing these requirements are identified and substantiated. Namely: in the implemented program, simple connected undirected graphs will be generated. We considered an important detail in working with graphs — graph traversal using the “Depth (width) search” algorithm, which in this task is used to check the graph for connectivity. The result of the work is presented — a software implementation of the graph generation algorithm in the C# programming language. In it, graphs are represented by an adjacency list, generated randomly, and checked for connectivity using the DFS (Depth First Search) function. DFS is a software implementation of the Depth First Search algorithm.

Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some partic-ular selection rule, and the analysis of the corre-sponding vertex orderings can aid greatly in de-vising algorithms, writing proofs of correctness, or recognition of various graph families. We study graphs where the sets of vertex order-ings produced by two di˙erent search methods coincide. We characterise such graph families for ten pairs from the best-known set of graph searches: Breadth First Search (BFS), Depth First Search (DFS), Lexicographic Breadth First Search (LexBFS) and Lexicographic Depth First Search (LexDFS), and Maximal Neighborhood Search (MNS).

Automated cell placement is a critical problem in very large scale integration (VLSI) physical design. New analytical placement methods that simultaneously spread cells and optimize wirelength have recently received much attention from both academia and industry. A novel and simple objective function for spreading cells over the placement area is described in the patent of Naylor et al. (U.S. Pat. 6301693). When combined with a wirelength objective function, this allows efficient simultaneous cell spreading and wirelength optimization using nonlinear optimization techniques. In this paper, we implement an analytic placer (APlace) according to these ideas (which have other precedents in the open literature), and conduct in-depth analysis of characteristics and extensibility of the placer. Our contributions are as follows. 1) We extend the objective functions described in (Naylor et al., U.S. Patent 6301693) with congestion information and implement a top-down hierarchical (multilevel) placer (APlace) based on them. For IBM-ISPD04 circuits, the half-perimeter wirelength of APlace outperforms that of FastPlace, Dragon, and Capo, respectively, by 7.8%, 6.5%, and 7.0% on average. For eight IBM-PLACE v2 circuits, after the placements are detail-routed using Cadence WRoute, the average improvement in final wirelength is 12.0%, 8.1%, and 14.1% over QPlace, Dragon, and Capo, respectively. 2) We extend the placer to address mixed-size placement and achieve an average of 4% wirelength reduction on ten ISPD'02 mixed-size benchmarks compared to results of the leading-edge solver, FengShui. 3) We extend the placer to perform timing-driven placement. Compared with timing-driven industry tools, evaluated by commercial detailed routing and static timing analysis, we achieve an average of 8.4% reduction in cycle time and 7.5% reduction in wirelength for a set of six industry testcases. 4) We also extend the placer to perform input/output-core coplacement and constraint handing for mixed-signal designs. Our paper aims to, and empirically demonstrates, that the APlace framework is a general, and extensible platform for spatial embedding tasks across many aspects of system physical implementation.

The concept of the minimum spanning tree (MST) plays an important role in topological network design, because it models a cheapest connected network. In a tree, however, the failure of a vertex can disconnect the network. In order to tolerate such a failure, we generalize the MST to the concept of a cheapest biconnected network. For a set of points in the Euclidean plane, we show that it is NP-hard to find a cheapest biconnected spanning graph, where edge costs are the Euclidean distances of the respective points. We propose a different type of subgraph, based on forbidding (due to failure) the use of a vertex. A minimum spanning multi-tree is a spanning graph that contains for each possible forbidden vertex a spanning tree that is minimum among the spanning trees that do not use the forbidden vertex. We propose a worst-case time optimal algorithm for computing a minimum spanning multi-tree for a planar Euclidean point set. A minimum spanning multi-tree is cheap, even though it embeds a linear number of MSTs: Its cost is more than the MST cost only by a constant factor. Furthermore, we propose a linear time algorithm for computing a cheap vertex failure tolerant graph, given the Delaunay triangulation. This graph bounds the cost of the minimum spanning multi-tree from above.

Control flow graph models program execution paths and is essential for program analysis and compiler optimizations. Compilers traverse thousands of graphs during compilation, thus, efficient control flow graph traversal is crucial. Prior work shows that breadth-first and depth-first search algorithms can perform differently depending on the graph structure, but the impact of graph features on the choice of the traversal algorithm remained underexplored. In this paper, we construct a dataset of over 200,000 control flow graphs extracted from modern JVM-based applications and train an ensemble-based machine learning model to predict the optimal graph traversal algorithm using only a set of lightweight graph features. Our model identifies the key features that drive accurate predictions, and we demonstrate that these informative features can be efficiently extracted during control flow graph construction.

Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space- and I/O-efficient algorithms are known for depth-first search or breadth-first search in sparse graphs. In this paper we present two new results on I/O-efficient depth-first search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new efficient depth-first search algorithm and show how planar depth-first search in general can be reduced to planar breadth-first search. As part of the first result we develop the first I/O-efficient algorithm for finding a simple cycle separator of a biconnected planar graph. Together with other recent reducibility results, the second result provides further evidence that external memory breadth-first search is among the hardest problems on planar graphs.

Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space- and I/O-efficient algorithms are known for depth-first search or breadth-first search in sparse graphs. In this paper we present two new results on I/O-efficient depth-first search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new efficient depth-first search algorithm and show how planar depth-first search in general can be reduced to planar breadth-first search. As part of the first result we develop the first I/O-efficient algorithm for finding a simple cycle separator of a biconnected planar graph. Together with other recent reducibility results, the second result provides further evidence that external memory breadth-firstsearch is among the hardest problems on planar graphs.KeywordsPlanar GraphExternal MemorySimple CycleOuterplanar GraphBoundary CycleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This review identifies graph traversal methods as fundamental steps in network analysis that facilitate easy examination of relations within the network. In this review, we plan to discuss multiple graph traversal approaches like depth first search (DFS), breadth first search (BFS), their varieties and indicate how these techniques can be used in practice when analyzing networks. The following is a review methodology covering 10 articles for years 2019 – 2024. The study responds to the question of how to select algorithms for various types of networks with reference to their computational cost and speed. Thus, the authors describe the advantages and drawbacks of the reported techniques, and the topics serve as recommendations for the further advancement of technology. In this respect, the present review also serves to help to close the divide between theory and practice.