Bidirectional Heuristic Search Reconsidered

The assessment of bidirectional heuristic search has been incorrect since it was first published more than a quarter of a century ago. For quite a long time, this search strategy did not achieve the expected results, and there was a major misunderstanding about the reasons behind it. Although there is still wide-spread belief that bidirectional heuristic search is afflicted by the problem of search frontiers passing each other, we demonstrate that this conjecture is wrong. Based on this finding, we present both a new generic approach to bidirectional heuristic search and a new approach to dynamically improving heuristic values that is feasible in bidirectional search only. These approaches are put into perspective with both the traditional and more recently proposed approaches in order to facilitate a better overall understanding. Empirical results of experiments with our new approaches show that bidirectional heuristic search can be performed very efficiently and also with limited memory. These results suggest that bidirectional heuristic search appears to be better for solving certain difficult problems than corresponding unidirectional search. This provides some evidence for the usefulness of a search strategy that was long neglected. In summary, we show that bidirectional heuristic search is viable and consequently propose that it be reconsidered.Comment: See http://www.jair.org/ for any accompanying file

Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions

It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose $f$-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called "surely expanded" (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions. We further prove that no admissible front-to-end algorithm has a worst case better than 2VC. Experimental results show that NBS competes with or outperforms existing bidirectional search algorithms, and often outperforms A* as well.Comment: Accepted to IJCAI 2017. Camera ready version with new timing result

Bidirectional A*: comparing balanced and symmetric heuristic methods

A widely known algorithm for ¯nding the shortest path in a network is Bidirectional A*. The version of bidirectional A* that is considered the most appropriatehitherto, uses so-called balanced heuristic estimates. In this paper, we focus on symmetric heuristic estimates. First, we show that bidirectional A* using the symmetricheuristic estimate provides us with a feasible approximation. Next a framework is introduced for solving the shortest path problem exactly. It turns out that both thebalanced and the symmetric heuristic estimate are instances of a general bidirectional A* framework. The symmetric instance surpasses the balanced instance in space andtime.operations research;graph theory;network flow;search;shortest path

Bidirectional A*: comparing balanced and symmetric heuristic methods

A widely known algorithm for ¯nding the shortest path in a network is Bidirectional A*. The version of bidirectional A* that is considered the most appropriate hitherto, uses so-called balanced heuristic estimates. In this paper, we focus on symmetric heuristic estimates. First, we show that bidirectional A* using the symmetric heuristic estimate provides us with a feasible approximation. Next a framework is introduced for solving the shortest path problem exactly. It turns out that both the balanced and the symmetric heuristic estimate are instances of a general bidirectional A* framework. The symmetric instance surpasses the balanced instance in space and time

Adaptively Informed Trees (AIT*): Fast Asymptotically Optimal Path Planning through Adaptive Heuristics

Informed sampling-based planning algorithms exploit problem knowledge for better search performance. This knowledge is often expressed as heuristic estimates of solution cost and used to order the search. The practical improvement of this informed search depends on the accuracy of the heuristic. Selecting an appropriate heuristic is difficult. Heuristics applicable to an entire problem domain are often simple to define and inexpensive to evaluate but may not be beneficial for a specific problem instance. Heuristics specific to a problem instance are often difficult to define or expensive to evaluate but can make the search itself trivial. This paper presents Adaptively Informed Trees (AIT*), an almost-surely asymptotically optimal sampling-based planner based on BIT*. AIT* adapts its search to each problem instance by using an asymmetric bidirectional search to simultaneously estimate and exploit a problem-specific heuristic. This allows it to quickly find initial solutions and converge towards the optimum. AIT* solves the tested problems as fast as RRT-Connect while also converging towards the optimum.Comment: IEEE International Conference on Robotics and Automation (ICRA) 2020, 6 + 2 pages, 5 figures, video available at https://youtu.be/twM723QM9T

Analisis dan Implementasi Algoritma IDA* (BIDA*) pada Pencarian Rute Optimum Angkutan Kota Bandung

ABSTRAKSI: Di Bandung setidaknya terdapat 44 trayek angkutan kota (angkot) baik dalam maupun antar kota. Ketika orang ingin bepergian menggunakan angkot, banyaknya trayek angkot ini sering kali justru membingungkan terutama bagi calon penumpang yang tidak familiar dengan trayek angkot Bandung seperti wisatawan atau pendatang baru. Metode pencarian yang sering digunakan pada kasus rute terpendek adalah algoritma A*. Namun ketika diimplementasikan pada ruang masalah yang besar A* membutuhkan memori penyimpanan yang besar pula. Iterative Deepening A* (IDA*) merupakan algoritma modifikasi dari A* yang mampu mengatasi masalah memori ini. Tetapi karena penulusuran dilakukan secara iteratif, IDA* harus membangkitkan simpul-simpul yang sama secara berulang, sehingga penghematan memori harus dibayar dengan pemborosan waktu eksekusi. Dengan kekurangan dan kelebihannya masing-masing, kedua algoritma ini tidak sesuai jika diterapkan pada perangkat mobile yang memiliki berbagai keterbatasan sumber daya. Dengan melakukan pencarian dari dua arah yaitu dari arah maju dan mundur, Bidirectional IDA* (BIDA*) mengkonsumsi memori lebih sedikit dibandingkan A*. Sedangkan dari sisi waktu eksekusi BIDA* lebih cepat daripada IDA*. Hasil akhir dari penelitian ini adalah BIDA* complete tetapi mungkin tidak optimal. Dari 50 pengujian terdapat 5 path yang solusinya tidak optimal dengan perbedaan jarak yang masih dapat diterima. Tetapi dari segi efektivitas BIDA* mengkonsumsi memori jauh lebih sedikit dibandingkan A* dengan waktu eksekusi yang jauh lebih cepat dibandingkan IDA*, sehingga dapat disimpulkan BIDA* mampu mengatasi kekurangan dua algoritma tersebut agar dapat diimplementasikan pada perangkat mobile. Kata Kunci : A*, IDA*, BIDA*, heuristik, memori, waktu eksekusiABSTRACT: There are at least 44 routes of Bandung public transportation (angkot), both within the city itself and between its neighboring cities. When people wants to travel by this angkot, those large number of routes frequently confusing especially for those who not familiar with the angkot routes of Bandung such as tourist or newcomers. A searching method that often used in shortest path cases is the A* algorithm. However, when implemented on a large problem space A* requires a large storage memory as well. Iterative Deepening A* (IDA*) is a modification of the A* algorithm that is able to overcome this memory problem. But for the searching done iteratively, IDA* must generate the same nodes repeatedly, thus saving memory should be paid to waste the time of execution. With the disadvantages and advantages of each, the two algorithms is not appropriat e when applied to mobile devices that have a variety of limited resources. By doing a search of two directions ie forward and backward, Bidirectional IDA* (BIDA*) consumes less memory than A* and in terms of execution time BIDA* is faster than IDA*. The end result of this research is to BIDA* complete but may not be optimal. Of the 50 tests there are 5 sub-optimal solution paths with the differences that still acceptable distance. But in terms of effectiveness BIDA* consumes much less memory than A * with execution time which is much faster than IDA*, so it can be concluded BIDA* is able to overcome these shortcomings for the two algorithms can be implemented on mobile devices. Keyword: A*, IDA*, BIDA*, heuristic, memory, time of executio

KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest. The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time $|E|^{\frac{1}{2}+o(1)}$ with high probability, obtaining a significant speedup with respect to the $\Theta(|E|)$ worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well. The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the $k$ most central nodes. Furthermore, our analysis is general, and it might be extended to other settings.Comment: Some typos correcte

Finding Shortest Paths With Computational Geometry

We present a heuristic search algorithm for the Rd Manhattan shortest path problem that achieves front-to-front bidirectionality in subquadratic time. In the study of bidirectional search algorithms, front-to-front heuristic computations were thought to be prohibitively expensive (at least quadratic time complexity); our algorithm runs in O(n logd n) time and O(n logd−1 n) space, where n is the number of visited vertices. We achieve this result by embedding the problem in Rd+1 and identifying heuristic calculations as instances of a dynamic closest-point problem, to which we then apply methods from computational geometry