We consider the deterministic path-planning problem dealing with the single-pair shortest path on a given graph. We propose a multiscale version of the well known A* algorithm (m-A*), which utilizes information of the environment at distinct scales. This information is collected via a bottom-up fusion method. Comparing with existing algorithms such as Dijkstra's or A*, the use of multiscale information leads to an improvement in terms of computational complexity.

Path-planning (equivalently, path-finding) problems are fundamental in many applications, such as transportation, VLSI design, robot navigation, and many more. In this paper, we consider dynamic shortest path-planning problems on a graph with a single endpoint pair and with potentially changing edge weights over time. Several algorithms exist in the literature that solve this problem, notably among them the Lifelong Planning algorithm. The algorithm is an incremental search algorithm that replans the path when there are changes in the environment. In numerical experiments, however, it was observed that the performance of is sensitive in the number of vertex expansions required to update the graph when an edge weight value changes or when a vertex is added or deleted. Although, in most cases, the classical requires a relatively small number of updates, in some other cases the amount of work required by the to find the optimal path can be overwhelming. To address this issue, in this paper, we propose an extension of the baseline algorithm, by making efficient use of a multiscale representation of the environment. This multiscale representation allows one to quickly localize the changed edges, and subsequently update the priority queue efficiently. This incremental multiscale ( for short) algorithm leads to an improvement both in terms of robustness and computational complexity-in the worst case-when compared to the classical . Numerical experiments validate the aforementioned claims.

Path-planning problems are fundamental in many applications, such as transportation, artificial intelligence, control of autonomous vehicles, and many more. In this paper, we consider the deterministic path-planning problem, equivalently, the single-pair shortest path problem on a given grid-like graph structure. Current commonly used algorithms in this area include the A algorithm, Dijkstra's algorithm, and their numerous variants.We propose an innovative beamlet-based graph structure for path planning that utilizes multiscale information of the environment. This information is collected via a bottom-up fusion algorithm. This new graph structure goes beyond "nearest-neighbor" connectivity, incorporating "long-distance" interactions between the nodes of the graph. Based on this new graph structure, we obtain a multiscale version of A , which is advantageous when preprocessing is allowable and feasible. Compared to the benchmark A algorithm, the use of multiscale information leads to an improvement in terms of computational complexity. Numerical experiments indicate an even more favorable behavior than the one predicted by the theoretical complexity analysis.Index Terms-A , beamlet-like structure, bottom-up fusion algorithm, Dijkstra's algorithm, dynamic programming, path-planning.

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Non-interactive zero-knowledge proof or argument (NIZK) systems are widely used in many security sensitive applications to enhance computation integrity, privacy and scalability. In such systems, a prover wants to convince one or more verifiers that the result of a public function is correctly computed without revealing the (potential) private input, such as the witness. In this work, we introduce a new notion, called scriptable SNARK, where the prover and verifier(s) can specify the function (or language instance) to be proven via a script. We formalize this notion in UC framework and provide a generic trusted hardware based solution. We then instantiate our solution in both SGX and Trustzone with Lua script engine. The system can be easily used by typical programmers without any cryptographic background. The benchmark result shows that our solution is better than all the known SNARK proof systems w.r.t. prover’s running time (1000 times faster), verifier’s running time, and the proof size. In addition, we also give a lightweight scriptable SNARK protocol for hardware with limited state, e.g., Θ ( λ ) bits. Finally, we show how the proposed scriptable SNARK can be readily deployed to solve many well-known problems in the blockchain context, e.g. verifier’s dilemma, fast joining for new players, etc.