Depth-first Search Tree Research Articles

Recognizing LBFS trees of bipartite graphs

The graph searches Breadth First Search (BFS) and Depth First Search (DFS) and the spanning trees constructed by them are some of the most basic concepts in algorithmic graph theory. BFS trees are first-in trees, i.e., every vertex is connected to its first visited neighbor. DFS trees are last-in trees, i.e., every vertex is connected to the last visited neighbor before it. The problem whether a given spanning tree can be the first-in tree or last-in tree of a graph search ordering was introduced in the 1980s and has been studied for several graph searches and graph classes. Here, we consider the problem of deciding whether a given spanning tree of a bipartite graph can be a first-in tree or a last-in tree of the Lexicographic Breadth First Search (LBFS), a special variant of BFS that is commonly used in graph algorithms. We show that the recognition of both first-in trees and last-in trees of LBFS is NP-hard even if the start vertex of the search ordering is fixed and the height of the tree is four. We prove that the bound on the height is tight (unless P=NP) by showing that for all spanning trees of bipartite graphs with height smaller than four we can solve both search tree recognition problems of LBFS in polynomial time. Finally, we give a linear-time algorithm that solves both problems for chordal bipartite graphs and fixed start vertices.

A few words about maps

In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a topological representation of maps with a given spanning quasi-tree using two fundamental polygons, which extends the representation of planar maps based on the equivalence with bipartite circle graphs. Then, we focus on Depth-First Search trees and their connection with a poset we define on the spanning quasi-trees of a map. We apply the bijections obtained in the first section to the problem of enumerating loopless rooted maps. Finally, we return to the planar case and discuss a decomposition of planar rooted loopless maps and its consequences on planar rooted loopless map enumeration.

Parallel distributed productivity‐aware tree‐search using Chapel

AbstractWith the recent arrival of the exascale era, modern supercomputers are increasingly big making their programming much more complex. In addition to performance, software productivity is a major concern to choose a programming language, such as Chapel, designed for exascale computing. In this paper, we investigate the design of a parallel distributed tree‐search algorithm, namely P3D‐DFS, and its implementation using Chapel. The design is based on the Chapel's DistBag data structure, revisited by: (1) redefining the data structure for Depth‐First tree‐Search (DFS), henceforth renamed DistBag‐DFS; (2) redesigning the underlying load balancing mechanism. In addition, we propose two instantiations of P3D‐DFS considering the Branch‐and‐Bound (B&B) and Unbalanced Tree Search (UTS) algorithms. In order to evaluate how much performance is traded for productivity, we compare the Chapel‐based implementations of B&B and UTS to their best‐known counterparts based on traditional OpenMP (intra‐node) and MPI+X (inter‐node). For experimental validation using 4096 processing cores, we consider the permutation flow‐shop scheduling problem for B&B and synthetic literature benchmarks for UTS. The reported results show that P3D‐DFS competes with its OpenMP baselines for coarser‐grained shared‐memory scenarios, and with its MPI+X counterparts for distributed‐memory settings, considering both performance and productivity‐awareness. In the context of this work, this makes Chapel an alternative to OpenMP/MPI+X for exascale programming.

Non-centralised coordinated optimisation for maximising offshore wind farm power via a sparse communication architecture

The motivation for establishing sparse communication architecture is to reduce the complexity and size of the power optimisation problem being solved by centralised controllers of a large-scale offshore wind farm. In this regard, this article introduced the sub-graph extraction technique to construct sparse communication architectures while ignoring the weakly coupled wake effects between turbines to develop two non-centralised coordination optimisation strategies for maximising power output. The non-centralised optimisation framework mainly uses the idea of graph decomposition that creates an original wake digraph by quantifying wake intensity, defining the spectral norm of the wake weight matrix as a constraint to obtain pruned wake sub-digraph. Then, for determining communication neighbours, we used a depth-first tree search arithmetic to cluster subsets of turbines by which the impact of neighbouring turbines was considered. On this basis, designing a suitable optimisation-based distributed or decentralised strategy, defining shared variables and consensus stages among the local controllers, yaw angles from such controllers are optimally coordinated to maximise the total power of the whole wind farm. Finally, a case study of a wind farm with 36 turbine simulation results showed that the scale of the non-convex optimisation problem could be efficiently reduced without affecting the power output while reducing execution time under various turbulence intensities.

Data Mining-based Fault Detection Method for Distributed Power Generation Systems

Traditional fault detection methods for power generation systems use cen-tralized fault processing analysis, which leads to long accuracy and responsetime of fault detection. To address these problems, a data mining-baseddistributed power generation system fault artificial intelligence detectionmethod is studied. The depth-first search tree algorithm is used to divide thegrid of distributed generation system. The network structure is modified tolocate fault zones by processing anomaly mining of the system data aftergrid division. The combination of fuzzy logic and wavelet singular entropyis used to complete the detection and identification of system faults. Throughsimulation experiments, it is verified that the response time of the detectionmethod is only 0.016 s, and its detection error rate and false negative rate are1.23% and 1.25%, which are far lower than other methods.

Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

Depth first search (DFS) tree is a fundamental data structure for solving various graph problems. The classical algorithm [54] for building a DFS tree requires O ( m + n ) time for a given undirected graph G having n vertices and m edges. Recently, Baswana et al. [5] presented a simple algorithm for updating the DFS tree of an undirected graph after an edge/vertex update in Õ( n ) 1 time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds that can be easily adopted to the parallel environment. In the parallel environment, a DFS tree can be computed from scratch in expected Õ(1) time [2] on an EREW PRAM, whereas the best deterministic algorithm takes Õ(√ n ) time [2, 27] on a CRCW PRAM. Our algorithm can be used to develop optimal time (to poly log n factors) deterministic parallel algorithms for maintaining fully dynamic DFS and fault tolerant DFS of an undirected graph. (1) Parallel Fully Dynamic DFS : Given an arbitrary online sequence of vertex or edge updates, we can maintain a DFS tree of an undirected graph in Õ(1) time per update using m processors on an EREW PRAM. (2) Parallel Fault tolerant DFS : An undirected graph can be preprocessed to build a data structure of size O ( m ), such that for any set of k updates (where k is constant) in the graph, a DFS tree of the updated graph can be computed in Õ(1) time using n processors on an EREW PRAM. For constant k , this is also work optimal (to poly log n factors). Moreover, our fully dynamic DFS algorithm provides, in a seamless manner, nearly optimal (to poly log n factors) algorithms for maintaining a DFS tree in the semi-streaming environment and a restricted distributed model. These are the first parallel, semi-streaming, and distributed algorithms for maintaining a DFS tree in the dynamic setting.

Space-Efficient Fully Dynamic DFS in Undirected Graphs †

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

Dynamic DFS in Undirected Graphs: Breaking the $O(m)$ Barrier

Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $...

ICI Cancellation Based on MIMO Decoding for FTN Non-Orthogonal FDM Systems

In this paper, we investigate multiple-input multiple-output (MIMO) decoding in faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) for inter-carrier interference (ICI) cancellation. The MIMO decoding is based on depth-first tree search or breadth-first tree search. The sphere decoder (SD) is a commonly used decoding algorithm based on the depth-first tree search. Maximum-likelihood detection with QR decomposition and M-algorithm (QRM-MLD) is a commonly used decoding algorithm based on the breadth-first tree search. By adding the initial radius to both SD and QRM-MLD, the computational complexity of these can be further decreased without the loss of the ICI cancellation performance. In the experiment, SD, QRM-MLD, and their corresponding simplified versions are used for the ICI cancellation in a 28-Gb/s FTN-NOFDM system with transmission over a 10-km standard single-mode fiber. The 3-dB equivalent bandwidth of this system is only approximately 5.5 GHz. Under serious high-frequency distortion caused by limited bandwidth, the bit error rate performance of the FTN-NOFDM can still reach the forward error correction limit due to the bandwidth compression and effective ICI cancellation. FTN-NOFDM with 20% and 30% bandwidth savings has approximately 1.3- and 1.1-dB improvements in receiver sensitivity compared to FTN-NOFDM with 10% bandwidth savings, respectively. To the best of our knowledge, this paper is the first experimental demonstration of the depth-first tree search and breadth-first tree search for FTN-NOFDM in a bandwidth-limited optical transmission system. The experimental results show that FTN-NOFDM is a promising scheme for bandwidth-limited systems.

DFS is Unsparsable and Lookahead Can Help in Maximal Matching

In this paper we study two problems in the context of fully dynamic graph algorithms that is, when we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph, preferably with a better time bound than that when running a classical algorithm from scratch each time a query arrives. In the first part we show that there are dense (directed) graphs having no nontrivial strong certificates for maintaining a depth-first search tree, hence the so-called sparsification technique cannot be applied effectively to this problem. In the second part, we show that a maximal matching can be maintained in an (undirected) graph with a deterministic amortized update cost of O(log m) (where m is the all-time maximum number of the edges), provided that a lookahead of length m is available, i.e. we can “take a peek” at the next m update operations in advance.

Low Complexity Iterative Receiver Design for Sparse Code Multiple Access

Sparse code multiple access (SCMA) is one of the most promising methods among all the non-orthogonal multiple access techniques in the future 5G communication. Compared with some other non-orthogonal multiple access techniques such as low density signature (LDS), SCMA can achieve better performance due to the shaping gain of the SCMA codewords. However, despite of the sparsity of the codewords, the decoding complexity of the current message passing algorithm (MPA) utilized by SCMA is still prohibitively high. In this paper, by exploring the lattice structure of SCMA codewords, we propose a low complexity decoding algorithm based on list sphere decoding (LSD). The LSD avoids the exhaustive search for all possible hypotheses and only considers signal within a hypersphere. As LSD can be viewed a depth-first tree search algorithm, we further propose several methods to prune the redundancy visited nodes in order to reduce the size of the search tree. Simulation results show that the proposed algorithm can reduce the decoding complexity substantially while the performance loss compared with the existing algorithm is negligible.

PERMAINAN CATUR INGGRIS BERBASIS ANDROID MENGGUNAKAN ALGORITMA MINIMAX

Today development of computer technology is growing rapidly, especialy in term of the game are certainly not stranger for the fans, from children to adults. The game has a positive impact that could indirectly hone the ability o f the brain and improve memory and patience. Catur Inggris is a strategy game like chess origin from Pekanbaru city, Riau province is generally played by two people, but more simple. Catur Inggris is based on Android with the programming C # language. Catur Inggris using Minimax algorithm with three difficulty levels that is, easy, medium, and hard. Minimax algorithm is an algorithm that using Depth-First Search method to find solutions step with limited depth. The results obtained from the test results using the algorithm method Minimax with Depth-First Search managed to generate possible winning position. Results obtained from tests using Minimax algorithm is 80% with five depth o f Depth-First Search tree four wins for the computer and a victory for the player, therefore Minimax algorithm can work well Catur Inggris game, and results test for user with 30 respondents get results 84%, therefore Catur Inggris game had a very good response from the users

Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs

Depth First Search (DFS) tree is a fundamental data structure for graphs used in solving various algorithmic problems. However, very few results are known for maintaining DFS tree in a dynamic environment--insertion or deletion of edges. We present the first algorithm for maintaining a DFS tree for an undirected graph under insertion of edges. For processing any arbitrary online sequence of edge insertions, this algorithm takes total $$O(n^2)$$O(n2) time.

A Novel Multiuser Detector Based on Restricted Search Space and Depth-First Tree Search Method in DS/CDMA Communication Systems

In this paper, we consider an improved and efficient algorithm for the multiuser detection (MUD) in direct sequence/code division multiple access (DS/CDMA) communication systems. The optimum detector for MUD is the maximum likelihood (ML) detector, but its complexity is very high and it calls for an optimization problem that involves an exhaustive search. Consequently, there has been considerable interest in suboptimal multiuser detectors with less complexity and reasonable performance. The idea of reducing the complexity by sub-optimum detectors was efficient and applicable but had some defects. The idea proposed in this paper is the restriction of the search space. This idea comprises using a sub-optimum detector such as ordinary genetic algorithm for which the size of the search space is confined to a predetermined region that is smaller than the whole search space. This limited region includes the objective bit sequence. Then by using depth-first tree search algorithm, we could find the optimum bit stream. We compare our algorithm to the ML detector, the genetic algorithm with conventional detector, and the ant colony optimization (ACO) detector which have been used for MUD in DS/CDMA. Simulation results show that the performance of this algorithm is near the optimal detector with very low complexity, and works better in comparison to other algorithms.

High-performance quadtree constructions on large-scale geospatial rasters using GPGPU parallel primitives

The increasingly available graphics processing units (GPU) hardware and the emerging general purpose computing on GPU (GPGPU) technologies provide an attractive solution to high-performance geospatial computing. In this study, we have proposed a parallel, primitive-based approach to quadtree construction by transforming a multidimensional geospatial computing problem into chaining a set of generic parallel primitives that are designed for one-dimensional (1D) arrays. The proposed approach is largely data-independent and can be efficiently implemented on GPGPUs. Experiments on 4096*4096 and 16384*16384 raster tiles have shown that the implementation can complete the quadtree constructions in 13.33 ms and 250.75 ms, respectively, on average on an NVidia GPU device. Compared with an optimized serial CPU implementation based on the traditional recursive depth-first search (DFS) tree traversal schema that requires 1191.87 ms on 4096*4096 raster tiles, a significant speedup of nearly 90X has been observed. The performance of the GPU-based implementation also suggests that an indexing rate in the order of more than one billion raster cells per second can be achieved on commodity GPU devices.

Concurrent Path Selection Algorithm in Statistical Timing Analysis

Circuit timing is becoming more and more uncertain under greater process variation as technology scales. Given the fault probability of each timing path and their statistical correlation from a statistical timing framework, the path selection problem for delay faults has a nature similar to the problem of designing a portfolio of stocks or assets or determining the size of bets in gambling to minimize risk. This observation allows us to develop a very different path selection approach from the conventional ones. If selection of k paths is required in a set of paths, we partition the set into two path sets and determine how many paths should be selected in each path set out of the k paths based on the probabilities of each path set containing faulty paths. We recursively continue this process, which results in the paths to be targeted during tests. The partitioning is easily performed because the paths are already grouped into the depth-first search tree based on their suffix or prefix. Experimental results show that the proposed algorithm can effectively use the correlation to generate high-quality path sets. In addition, we study the issues that occur after automatic test pattern generation on the selected paths, and discuss possible solutions to them.

Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways.

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold , , , and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an , , and knotted protein. An overlap parameter is defined between pathways; we find that proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.

Lower Bound on Expected Complexity of Depth-First Tree Search with Multiple Radii

Depth-first tree search with multiple radii (DFTS-MR) algorithm attains significant complexity reduction over DFTS with a single radius (DFTS-SR) for solving integer least-squares (ILS) problems. Herein, we derive the lower bound on the expected complexity of DFTS-MR under i.i.d. complex Gaussian environments. Currently, the upper bound on the expected DFTS-MR complexity is known. Our analytical result shows the computational dependence on the statistics of the channel, the noise, and the transmitted symbols. It also reflects the use of multiple radii, which is one of the main characteristics of DFTS-MR. The resultant lower bound provides an efficient means to better understand the complexity behavior of DFTS-MR, along with the (known) upper bound.

Efficient Representation of Constraints and Propagation of Variable-Value Symmetries in Distributed Constraint Reasoning

In this paper, we discuss variable and value symmetries in distributed constraint reasoning and efficient methods to represent and propagate them in distributed environments. Unlike commonly used centralised methods which detect symmetries according to their global definition, we suggest here to define them at the individual constraint level, then define operations on those symmetries in order to propagate them through the depth-first search tree that is generated in efficient distributed constraint reasoning algorithms. In our algorithm, we represent constraints (or utility functions) by a list of costs: while the usual representation lists one cost for one assignation, we drastically reduce the size of that list by keeping only one cost for one class of equivalence of assignations. In practice, for a constraint with n symmetric variables defined on a domain of n symmetric values, this approach cuts down the size of the list of costs from nn to p(n) (partition function of n), i.e., from 1010 to 42 when n = 10. We henceforth devised algorithms to process the sparse representations of utility functions and to propagate them along with symmetry information among distributed agents. We implemented this new representation of constraints and tested it with the DPOP algorithm on distributed graph colouring problems, rich in symmetries. Our evaluation shows that in 19% of execution instances we cut down 10 times the volume of communication spent, while no significant overhead appears in non symmetrical executions. These results open serious perspectives on a possible bounding of memory and communication bandwidth consumption in some subclass of distributed constraint reasoning problems.

A self-stabilising algorithm for 3-edge-connectivity

Self-stabilisation is a theoretical framework for fault-tolerance without external assistance. Adoption of self-stabilisation in distributed systems has received considerable research interest over the last decade. In this paper, we propose a self-stabilising algorithm for 3-edge-connectivity of an asynchronous distributed model of computation. A self-stabilising depth-first search algorithm is run concurrently to build a depth-first search spanning tree of the system. Once such a tree is constructed, all the 3-edge-connected components of the system can be detected in O ( h ) rounds, where h is the height of the depth-first search tree. The result of computation is kept in a distributed fashion in the sense that, upon stabilisation of the algorithm, each processor knows all other processors that are 3-edge-connected to it. The space complexity of our algorithm is O ( n 2 log Δ) bits per processor, where Δ is an upper bound on the degree of a processor.