Bidirectional Algorithms Research Articles

Efficient Personalized PageRank Computation: The Power of Variance-Reduced Monte Carlo Approaches

Personalized PageRank (PPR) computation is a fundamental problem in graph analysis. The state-of-the-art algorithms for PPR computation are based on a bidirectional framework which include a deterministic forward push and a Monte Carlo sampling procedure. The Monte Carlo sampling procedure, however, often has a relatively-large variance, thus reducing the performance of the PPR computation algorithms. To overcome this issue, we develop two novel variance-reduced Monte Carlo techniques for PPR computation. Our first technique is to apply power iterations to reduce the variance of the Monte Carlo sampling procedure. We prove that conducting few power iterations can significantly reduce the variance of existing Monte Carlo estimators, only with few additional costs. Moreover, we show that such a simple and novel variance-reduced Monte Carlo technique can achieve comparable estimation accuracy and the same time complexity as the state-of-the-art bidirectional algorithms. Our second technique is a novel progressive sampling method which uses the historical information of former samples to reduce the variance of the Monte Carlo estimator. We develop several novel PPR computation algorithms by integrating both of these variance reduction techniques with two existing Monte Carlo sampling approaches, including random walk sampling and spanning forests sampling. Finally, we conduct extensive experiments on 5 real-life large graphs to evaluate our solutions. The results show that our algorithms can achieve much higher PPR estimation accuracy by using much less time, compared to the state-of-the-art bidirectional algorithms.

Iterative Deepening Dynamically Improved Bounds Bidirectional Search

This paper presents a new bidirectional search algorithm to solve the shortest path problem. The new algorithm uses an iterative deepening technique with a consistent heuristic to improve lower bounds on path costs. The new algorithm contains a novel technique of filtering nodes to significantly reduce the memory requirements. Computational experiments on the pancake problem, sliding tile problem, and Rubik’s cube show that the new algorithm uses significantly less memory and executes faster than A* and other state-of-the-art bidirectional algorithms. Summary of Contribution: Quickly solving single-source shortest path problems on graphs is important for pathfinding applications and is a core problem in both artificial intelligence and operations research. This paper attempts to solve large problems that do not easily fit into the available memory of a desktop computer, such as finding the optimal shortest set of moves to solve a Rubik’s cube, and solve them faster than existing algorithms.

Minimizing Node Expansions in Bidirectional Search with Consistent Heuristics

A* is optimally effective with regard to node expansions among unidirectional admissible algorithms—those that only assume that the heuristic used is admissible. Among bidirectional algorithms the Fractional MM algorithm is optimally effective (given the correct parameters) among admissible algorithms.This paper generalizes the bidirectional result to more complex settings where more information on the problem domain can be exploited: (1) When the cost of the minimal edge is known. (2) When the algorithm knows that the heuristics are consistent. This characterization uses a novel algorithm called MT. MT is similar to Fractional MM and is also optimally effective, but simpler to analyze.

Dynamically improved bounds bidirectional search

This paper presents a bidirectional search algorithm that dynamically improves the bounds during its execution. It has the property that it always terminates on or before the forward search meets the backward search. Computational experiments on the pancake problem, the sliding tile puzzle, and the topspin problem demonstrate that it is capable of solving problems using significantly fewer node expansions than A⁎ or state-of-the-art bidirectional algorithms such as MMϵ and GBFHS.

Agent-based bidirectional charging algorithms for battery electric vehicles in renewable energy communities

This paper introduces a framework for agent based autonomous charging and discharging of Battery Electric Vehicle (BEV) at local energy communities. Agents are programmed to control the bidirectional charging according to green energy utilisation incentives, based on load and generation forecasts. The optimization is achieved within a group of independent prosumers following a fully distributed approach using multiple self-organising agents. No central instance is needed for communication, billing or decision making. To demonstrate the ecological benefits of the system, simulations for a car pool, with a Photovoltaic (PV) plant, in a residential neighborhood were performed. The simulations resulted in an increased community PV self-consumption value of 48% compared to 29% in case of uncontrolled charging processes.

Predicting the Effectiveness of Bidirectional Heuristic Search

The question of when bidirectional heuristic search outperforms unidirectional heuristic search has been revisited numerous times in the field of Artificial Intelligence. This paper re-addresses the question of when bidirectional search outperforms unidirectional search using an updated theoretical understanding of the problem. We show that a core set of critical states in the state space are the primary factor determining whether a bidirectional search can outperform a unidirectional search and provide simple measures to determine whether a state space and heuristic contains these critical states. We similarly discuss and show the impact that asymmetry in the underlying problem graph has on the performance of bidirectional algorithms. Experimental results show the impact of these factors on whether a problem should be solved using unidirectional or bidirectional search.

A Unifying View on Individual Bounds and Heuristic Inaccuracies in Bidirectional Search

In the past few years, new very successful bidirectional heuristic search algorithms have been proposed. Their key novelty is a lower bound on the cost of a solution that includes information from the g values in both directions. Kaindl and Kainz (1997) proposed measuring how inaccurate a heuristic is while expanding nodes in the opposite direction, and using this information to raise the f value of the evaluated nodes. However, this comes with a set of disadvantages and remains yet to be exploited to its full potential. Additionally, Sadhukhan (2013) presented BAE∗, a bidirectional best-first search algorithm based on the accumulated heuristic inaccuracy along a path. However, no complete comparison in regards to other bidirectional algorithms has yet been done, neither theoretical nor empirical. In this paper we define individual bounds within the lower-bound framework and show how both Kaindl and Kainz's and Sadhukhan's methods can be generalized thus creating new bounds. This overcomes previous shortcomings and allows newer algorithms to benefit from these techniques as well. Experimental results show a substantial improvement, up to an order of magnitude in the number of necessarily-expanded nodes compared to state-of-the-art near-optimal algorithms in common benchmarks.

Bidirectional scale-invariant feature transform feature matching algorithms based on priority k-d tree search

In this article, a bidirectional feature matching algorithm and two extended algorithms based on the priority k-d tree search are presented for the image registration using scale-invariant feature transform features. When matching precision of image registration is below 50%, the discarding wrong match performance of many robust fitting methods like Random Sample Consensus (RANSAC) is poor. Therefore, improving matching precision is a significant work. Generally, a feature matching algorithm is used once in the image registration system. We propose a bidirectional algorithm that utilizes the priority k-d tree search twice to improve matching precision. There are two key steps in the bidirectional algorithm. According to the case of adopting the ratio restriction of distances in the two key steps, we further propose two extended bidirectional algorithms. Experiments demonstrate that there are some special properties of these three bidirectional algorithms, and the two extended algorithms can achieve higher precisions than previous feature matching algorithms.

Bidirectional algorithms for interference suppression in multiuser systems

This paper presents adaptive bidirectional minimum mean-square error parameter estimation algorithms for fast-fading channels. The time correlation between successive channel gains is exploited to improve the estimation and tracking capabilities of adaptive algorithms and provide robustness against time-varying channels. Bidirectional normalized least mean-square and conjugate gradient algorithms are devised along with adaptive mixing parameters that adjust to the time-varying channel correlation properties. An analysis of the proposed algorithms is provided along with a discussion of their performance advantages. Simulations for an application to interference suppression in multiuser DS-CDMA systems show the advantages of the proposed algorithms.

The affix array data structure and its applications to RNA secondary structure analysis

Efficient string-processing in large data sets like complete genomes is strongly connected to the suffix tree and similar index data structures. With respect to complex structural string analysis like the search for RNA secondary structure patterns, unidirectional suffix tree algorithms are inferior to bidirectional algorithms based on the affix tree data structure. The affix tree incorporates the suffix tree and the suffix tree of the reverse text in one tree structure but suffers from its large memory requirements. In this paper I present a new data structure, denoted affix array, which is equivalent to the affix tree with respect to its algorithmic functionality, but with smaller memory requirements and improved performance. I will show a linear time construction of the affix array without making use of the linear time construction of the affix tree. I will also show how bidirectional affix tree traversals can be transferred to the affix array and present the impressive results of large scale RNA secondary structure analysis based on the new data structure.

Creating high-fidelity images – a convolution approach to gridding airborne data using a SINC kernel

Airborne geophysical data sampled at a constant time-interval along lines and with a nominal spatial-separation across lines are quasi-periodic and are therefore amenable to interpolation onto a regular grid by convolving the original line data with a 2D SINC kernel. This method has advantages over commonly used minimum curvature or bidirectional gridding algorithms because it better maintains the spatial fidelity of the original data as per the sampling theorem. Unlike splines, the SINC function does not suffer from over- interpolation, although ringing can be problematic. Lastly, the smooth SINC kernel places no lower bound on cell sizes, except computation time. The method first uses a 1D SINC interpolation to resample the along-line data. An SVD matrix inversion is then used to move each line from its true to its nominal location before interpolating the inter-line areas of the grid with the 2D kernel. Ringing and aliasing are mitigated by employing a window function to dampen the effects of the ideal RECT function in the wavenumber domain. Through judicious selection of the along- and across-line maximum wavenumbers, the SINC kernel can improve the continuity of lineaments trending obliquelyto the flight lines.

Route planning for automated guided vehicles in a manufacturing facility

Automated guided vehicles (AGVs) are widely used in manufacturing and transporting facilities for the movement of material from one location to another. Research in this area is directed toward the development of a path layout design and routing algorithms for movements of materials. The problem is to design a path layout and a routing algorithm that will route the AGVs along the bi-directional path so that the distance travelled will be minimized. This paper presents a bi-directional path flow layout and a routing algorithm that guarantee conflict-free, shortest-time routes for AGVs. Based on the path layout, a routing algorithm and sufficient, but necessary, conditions, mathematical relationships are developed among certain key parameters of vehicle and path. A high degree of concurrency is achieved in vehicle movement. Routing efficiency is analysed in terms of the distance travelled and the time required for AGVs to complete all pickup and drop-off jobs. Numerical results are presented to compare the performance of the proposed model. The research provides the foundation for a bi-directional path layout design and routing algorithms that will aid the designer to develop complicated path layouts.

BIDA ∗: an improved perimeter search algorithm

In this paper we present a new bidirectional heuristic search algorithm. Our algorithm can be viewed as a perimeter search algorithm, and it uses a new technique for reducing the number of heuristic evaluations. We also prove some general results on the behavior of iterative deepening perimeter search algorithms, and we discuss some new ‘lazy evaluation’ techniques for improving their performance. The theoretical and experimental results show that perimeter search algorithms outperform the other bidirectional algorithms, and we believe it is worthwhile to give them a deep look in subsequent research.

Distributed Algorithms For Unidirectional Networks

This paper addresses the question of distributively computing over a strongly connected unidirectional data communication network. In unidirectional networks the existence of a communication link from one node to another does not imply the existence of a link in the opposite direction. The strong connectivity means that from every node there is a directed path to any other node. The authors assume an arbitrary topology network in which the strong connectivity is the only restriction. Four models are considered, synchronous and asynchronous, and for each node space availability, which grows as either $O(1)$ bits or $O(\log n)$ bits per incident link, where n is the total number of nodes in the network, is considered. First algorithms for two basic problems in distributed computing in data communication networks, traversal, and election, are provided. Each of these basic protocols produces two directed spanning trees rooted at a distinguished node in the network, one called in-tree, leading to the root, and the other, out-tree, leading from the root. Given these trees, the authors efficiently transform bidirectional algorithms to run on unidirectional networks, and in particular solve other problems such as the broadcast and echo [E. J. CHANG, Decentralized Algorithms in Distributed Systems, Ph.D. thesis, University of Toronto. October 19791 in a way that is more efficient $O(n^2 )$ messages) than direct transformation (which yields $O(nm)$ messages algorithm). The communication cost of the traversal and election algorithms is $O(nm + n^2 \log n)$ bits ($O(nm)$ messages and time), where m is the total number of links in the network. The traversal algorithms for unidirectional networks of finite automata achieve the same cost $O(nm + n^2 \log n)$ bits ($O(nm)$ messages and time) bits) in the asynchronous case, while in the synchronous case the communication cost of the algorithm is ($O(nm)$ bits.

Bidirectional breadth-first algorithms for the decoding of convolutional codes

Bidirectional multiple-path tree searching algorithms for the decoding of convolutional codes are presented. These suboptimal coding algorithms use a multiple-path breadth-first bidirectional tree exploration procedure and long-memory convolution codes. It is shown that, compared to the usual M-algorithm, the bidirectional exploration considerably reduces the bit error propagation due to correct path loss. Computer simulations using rate-1/2 codes over binary symmetric channels are used to analyze the effect of the number of path extensions, code memory, and frame length on the bit error probability. The results show that with a bit error probability of 10/sup -5/, coding gains on the order of 2 dB over the M-algorithm and 1 dB over a Viterbi decoder of equivalent complexity can be achieved. >

BS ∗: An admissible bidirectional staged heuristic search algorithm

In order to reap the potential advantage of less extensive searching which bidirectional heuristic search algorithms offer, strategies are needed to influence the two search wavefronts to meet such that early termination will occur. The principled search control strategy aims to achieve this without trading running time, but can be found wanting still. An improved algorithm BS∗ is described which expands significantly less nodes on average than any other algorithm in the same class of non-wave-shaping admissible bidirectional algorithms. When pitted against BHPA, the only other heuristically guided member in this class, BS∗'s average search efficiency in time and space is about 30% better. BS∗'s superior performance stems from the use of all opportunities to achieve early termination and the elimination of unfruitful avenues by search reduction operations: nipping, pruning, trimming and screening. Such operations exploit information gathered during search and have several spin-offs: more accurate guidance of search control, early exposure of nonpromising nodes and reduced bookkeeping overheads, all of which further enhance BS∗'s performance. A further noteworthy feature of BS∗ is that it is the first staged search algorithm which preserves admissibility.

Analysis of a distributed algorithm for extrema finding in a ring

A new and more detailed analysis of the unidirectional algorithm of Chang and Roberts for distributed extrema finding on a ring is presented. This analysis shows that this simple algorithm, which is known to be average case optimal, compares very favorably with all the other known algorithms as it requires O( n log n) messages with probability tending to one. A bidirectional version of this algorithm is presented and is shown to dominate the unidirectional one in its average message complexity. Finally, both the unidirectional and the bidirectional algorithms are generalized to perform k selection in the ring, i.e., find the k largest labeled processors.