Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms. While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.

In recent years the understanding of optimal bidirectional heuristic search (BiHS) has progressed significantly. Yet, Bi-HS is relatively unexplored in unbounded suboptimal search. Front-to-end (F2E) and front-to-front (F2F) bidirectional search have been used in optimal algorithms, but adapting them for unbounded suboptimal search remains an open challenge. We introduce a framework for suboptimal BiHS, called anchor search, and use it to derive a parameterized family of algorithms. Because our new algorithms need F2F heuristic evaluations, we propose using pattern databases (PDBs) as differential heuristics (DHs) to construct F2F heuristics. Our experiments evaluate three anchor search instances across diverse domains, outperforming existing methods, particularly as the search scales.

Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms. While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.

BAE*, and the independently developed DIBBS, are state-of-the-art bidirectional heuristic search algorithms that exploit heuristic consistency to efficiently prove solution optimality. Historically, BAE* has been studied with various direction-selection policies, determining whether to expand the next state from the forward or backward search. However, some of these policies expand nodes with an f-value exceeding the optimal solution cost, C*, which clearly cannot be part of any optimal solution. In this position paper, we review direction-selection strategies in BAE* and bidirectional search more broadly, analyzing their impact on the behavior of the search. Additionally, we present a low-overhead solution that prevents the expansion of nodes with f > C* across all direction-selection strategies.

In heuristic search, it is well-established that different types of heuristics are suited for optimal heuristic search (OHS) and unbounded suboptimal search (USS). In OHS, the heuristic should minimize the error in estimating the true cost of the shortest path, whereas in USS, it is more beneficial for the heuristic to exhibit a clear gradient toward the goal, regardless of the error. However, no study has specifically investigated which heuristic is most effective for bounded suboptimal search (BSS), and the current standard is to use heuristics designed for OHS. This paper introduces a novel method for creating heuristics tailored to BSS by linearly combining heuristics that were designed for OHS and USS. Through experimental evaluation, the proposed method is compared with those suited for OHS and USS. The results demonstrate that, within certain suboptimality bounds, our new heuristic approach outperforms OHS and USS heuristics for various BSS algorithms.

Recent research on bidirectional heuristic search (BiHS) has been shaped by the must-expand pairs (MEP) theory, which identifies the pairs of nodes that must be expanded to ensure solution optimality. Another line of research has focused on algorithms utilizing lower bounds derived from consistent heuristics during the search. This paper bridges these two approaches, offering a unified framework that demonstrates how both existing and novel algorithms can be derived from MEP theory. We introduce an extended set of bounds, encompassing both previously known and newly formulated ones. Using these bounds, we develop a range of algorithms, each employing different criteria for termination, node selection, and search direction. Finally, we empirically evaluate how these bounds and algorithms impact search efficiency.

Parallelization and External Memory (PEM) techniques have significantly enhanced the capabilities of search algorithms when solving large-scale problems. Previous research on PEM has primarily centered on unidirectional algorithms, with only one publication on bidirectional PEM that focuses on the meet-in-the-middle (MM) algorithm. Building upon this foundation, this paper presents a framework that integrates both uni- and bi-directional best-first search algorithms into this framework. We then develop a PEM variant of the state-of-the-art bidirectional heuristic search (BiHS) algorithm BAE* (PEM-BAE*). As previous work on BiHS did not focus on scaling problem sizes, this work enables us to evaluate bidirectional algorithms on hard problems. Empirical evaluation shows that PEM-BAE* outperforms the PEM variants of A* and the MM algorithm, as well as a parallel variant of IDA*. These findings mark a significant milestone, revealing that bidirectional search algorithms clearly outperform unidirectional search algorithms across several domains, even when equipped with state-of-the-art heuristics.

While most work in heuristic search concentrates on goal-specific heuristics, which estimate the shortest path cost from any state to the goal, we explore all-pair heuristics that estimate distances between all pairs of states. We examine the relationship between these heuristic functions and the shortest distance function they estimate, revealing that all-pair consistent heuristics may violate the triangle inequality. Thus, we introduce a new property for heuristics called Δ-consistency, requiring adherence to the triangle inequality. Additionally, we present a method for transforming standard consistent heuristics to be Δ-consistent, showcasing its benefits through a synthetic example. We then show that common heuristic families inherently exhibit Δ-consistency. This positive finding encourages the use of all-pair consistent heuristics, and prompts further investigation into the optimality of A*, when given an all-pair heuristic instead of a goal-specific heuristic.

Parallelization and External Memory (PEM) techniques significantly enhance the capabilities of search algorithms for solving large-scale problems. While previous research on PEM has primarily centered on unidirectional algorithms, this work presents a versatile PEM framework that integrates both uni- and bi-directional best-first search algorithms.

QUIC is a UDP-based application-level transport protocol implementing TCP-like properties. QUIC is optimized toward web activities such as HTTP and HTTPS, and is gaining rapid popularity as most Google clients use this protocol to access Google's services. However, despite its popularity, we still lack an in-depth understanding of QUIC's performance in various network environments. While the existing work evaluates QUIC in multiple scenarios, we do not have sufficient knowledge to derive a predictive performance model for QUIC and remain mainly with a few anecdotes. Based on an exploratory analysis of the effects of various parameters on QUIC's behavior, our work characterizes QUIC's performance and develops a predictive model, providing insights into the main parameters affecting QUIC's performance, such as loss, packet reordering, and latency. The resulted predictive model opens the door for future optimization and protocol design.

Recent research on bidirectional heuristic search (BiHS) is based on the must-expand pairs theory (MEP theory), which describes which pairs of nodes must be expanded during the search to guarantee the optimality of solutions. A separate line of research in BiHS has proposed algorithms that use lower bounds that are derived from consistent heuristics during search. This paper links these two directions, providing a comprehensive unifying view and showing that both existing and novel algorithms can be derived from the MEP theory. An extended set of bounds is formulated, encompassing both previously discovered bounds and new ones. Finally, the bounds are empirically evaluated by their contribution to the efficiency of the search

Most recent theoretical and algorithmic work in bidirectional heuristic search (BiHS) used front-to-end (F2E) heuristics that estimate the distance to the start and goal states. In this paper, we start exploring front-to-front (F2F) heuristics, which estimate the distance between any pair of states. Devising efficient algorithms that use F2F heuristics is a challenging task. Thus, it is important to first understand the benefits of using F2F heuristics compared to F2E heuristics. To this end, we theoretically and experimentally demonstrate that there is a great potential in using F2F heuristics implying that F2F BiHS is a promising area of future research.