Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

An approach to quantum-computational hydrologic inverse analysis.

https://publikationen.bibliothek.kit.edu/1000137076/126360194

SAT Competition 2020

Prior approaches for finding the longest simple path (LSP) in a graph used constraints solvers and genetic algorithms In this work, we solve the LSP problem with heuristic search We first introduce several methods for pruning dominated path prefixes Then, we propose several admissible heuristic functions for this problem Experimental results demonstrate the large impact of the proposed heuristics and pruning rules

/pdf/solving-the-longest-simple-path-problem-with-heuristic-1cs6ge0j70.pdf

Solving the Longest Simple Path Problem with Heuristic Search.

Embedding an interconnection network into another network is one of the important problems in parallel processing. In this paper, we study embedding of linear arrays (paths) of maximum length in O-shaped meshes (O-shaped grid graphs). This is equal to finding a longest path in an O-shaped mesh (grid graph). An O-shaped mesh is a 2D mesh that a smaller 2D mesh is removed from it. The removed nodes can be considered as faulty processor. We give a linear-time parallel algorithm for this problem. To show the algorithm finds an optimal path, first we prove some upper bounds on the length of the longest paths, then we show that how our algorithm meets these upper bounds.

Embedding linear arrays of the maximum length in O-shaped meshes

An approach to quantum-computational hydrologic inverse analysis

We propose an exact algorithm for solving the longest path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that were previously unsolved and solve hard instances significantly faster. We also present a parallel version of the algorithm.

Finding Optimal Longest Paths by Dynamic Programming in Parallel

We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that were previously unsolved and solve hard instances significantly faster. Lastly, we present a scalable parallelization which yields the first efficient parallel algorithm for the problem.

Finding Optimal Longest Paths by Dynamic Programming in Parallel.

We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that have previously been unsolved.

Kai Fieger

Papers

Finding Optimal Longest Paths by Dynamic Programming in Parallel

Finding Optimal Longest Paths by Dynamic Programming in Parallel.

Optimal Longest Paths by Dynamic Programming