Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the dynamic setting, where (1) we have oracle access to a monotone submodular function $f: 2^{V} \rightarrow \mathbb{R}^+$ and (2) we are given a sequence $\mathcal{S}$ of insertions and deletions of elements of an underlying ground set $V$. We develop the first fully dynamic $(4+\epsilon)$-approximation algorithm for the submodular maximization problem under the matroid constraint using an expected worst-case $O(k\log(k)\log^3{(k/\epsilon)})$ query complexity where $0 < \epsilon \le 1$. This resolves an open problem of Chen and Peng (STOC'22) and Lattanzi et al. (NeurIPS'20). As a byproduct, for the submodular maximization under the cardinality constraint $k$, we propose a parameterized (by the cardinality constraint $k$) dynamic algorithm that maintains a $(2+\epsilon)$-approximate solution of the sequence $\mathcal{S}$ at any time $t$ using an expected worst-case query complexity $O(k\epsilon^{-1}\log^2(k))$. This is the first dynamic algorithm for the problem that has a query complexity independent of the size of ground set $V$.

The escalating size of Deep Neural Networks (DNNs) has spurred a growing research interest in hosting and serving DNN models across multiple devices. A number of studies have been reported to partition a DNN model across devices, providing device placement solutions. The methods appeared in the literature, however, either suffer from poor placement performance due to the exponential search space or miss an optimal placement as a consequence of the reduced search space with limited heuristics. Moreover, these methods have ignored the runtime inter-operator optimization of a computation graph when coarsening the graph, which degrades the end-to-end inference performance. This paper presents Moirai that better exploits runtime inter-operator fusion in a model to render a coarsened computation graph, reducing the search space while maintaining the inter-operator optimization provided by inference backends. Moirai also generalizes the device placement algorithm from multiple perspectives by considering inference constraints and device heterogeneity.Extensive experimental evaluation with 11 large DNNs demonstrates that Moirai outperforms the state-of-the-art counterparts, i.e., Placeto, m-SCT, and GETF, up to 4.28$\times$ in reduction of the end-to-end inference latency. Moirai code is anonymously released at \url{https://github.com/moirai-placement/moirai}.

In Weighted Model Counting (WMC), we assign weights to literals and compute the sum of the weights of the models of a given propositional formula where the weight of an assignment is the product of the weights of its literals. The current WMC solvers work on Conjunctive Normal Form (CNF) formulas. However, CNF is not a natural representation for human-being in many applications. Motivated by the stronger expressive power of pseudo-Boolean (PB) formulas than CNF, we propose to perform WMC on PB formulas. Based on a recent dynamic programming algorithm framework called ADDMC for WMC, we implement a weighted PB counting tool PBCounter. We compare PBCounter with the state-of-the-art weighted model counters SharpSAT-TD, ExactMC, D4, and ADDMC, where the latter tools work on CNF with encoding methods that convert PB constraints into a CNF formula. The experiments on three domains of benchmarks show that PBCounter is superior to the model counters on CNF formulas.

Constraint Optimization Problems (COP) pose intricate challenges in combinatorial problems usually addressed through Branch and Bound (B\&B) methods, which involve maintaining priority queues and iteratively selecting branches to search for solutions. However, conventional approaches take a considerable amount of time to find optimal solutions, and it is also crucial to quickly identify a near-optimal feasible solution in a shorter time. In this paper, we aim to investigate the effectiveness of employing a depth-first search algorithm for solving COP, specifically focusing on identifying optimal or near-optimal solutions within top $n$ solutions. Hence, we propose a novel heuristic neural network algorithm based on MCTS, which, by simultaneously conducting search and training, enables the neural network to effectively serve as a heuristic during Backtracking. Furthermore, our approach incorporates encoding COP problems and utilizing graph neural networks to aggregate information about variables and constraints, offering more appropriate variables for assignments. Experimental results on stochastic COP instances demonstrate that our method identifies feasible solutions with a gap of less than 17.63% within the initial 5 feasible solutions. Moreover, when applied to attendant Constraint Satisfaction Problem (CSP) instances, our method exhibits a remarkable reduction of less than 5% in searching nodes compared to state-of-the-art approaches.

An efficient robot path-planning model is vulnerable to the number of search nodes, path cost, and time complexity. The conventional A-star (A*) algorithm outperforms other grid-based algorithms for its heuristic search. However it shows suboptimal performance for the time, space, and number of search nodes, depending on the robot motion block (RMB). To address this challenge, this study proposes an optimal RMB for the A* path-planning algorithm to enhance the performance, where the robot movement costs are calculated by the proposed adaptive cost function. Also, a selection process is proposed to select the optimal RMB size. In this proposed model, grid-based maps are used, where the robot's next move is determined based on the adaptive cost function by searching among surrounding octet neighborhood grid cells. The cumulative value from the output data arrays is used to determine the optimal motion block size, which is formulated based on parameters. The proposed RMB significantly affects the searching time complexity and number of search nodes of the A* algorithm while maintaining almost the same path cost to find the goal position by avoiding obstacles. For the experiment, a benchmarked online dataset is used and prepared three different dimensional maps. The proposed approach is validated using approximately 7000 different grid maps with various dimensions and obstacle environments. The proposed model with an optimal RMB demonstrated a remarkable improvement of 93.98% in the number of search cells and 98.94% in time complexity compared to the conventional A* algorithm. Path cost for the proposed model remained largely comparable to other state-of-the-art algorithms. Also, the proposed model outperforms other state-of-the-art algorithms.

Existing view planning systems either adopt an iterative paradigm using next-best views (NBV) or a one-shot pipeline relying on the set-covering view-planning (SCVP) network. However, neither of these methods can concurrently guarantee both high-quality and high-efficiency reconstruction of 3D unknown objects. To tackle this challenge, we introduce a crucial hypothesis: with the availability of more information about the unknown object, the prediction quality of the SCVP network improves. There are two ways to provide extra information: (1) leveraging perception data obtained from NBVs, and (2) training on an expanded dataset of multiview inputs. In this work, we introduce a novel combined pipeline that incorporates a single NBV before activating the proposed multiview-activated (MA-)SCVP network. The MA-SCVP is trained on a multiview dataset generated by our long-tail sampling method, which addresses the issue of unbalanced multiview inputs and enhances the network performance. Extensive simulated experiments substantiate that our system demonstrates a significant surface coverage increase and a substantial 45% reduction in movement cost compared to state-of-the-art systems. Real-world experiments justify the capability of our system for generalization and deployment.

This paper introduces a sampling-based strategy synthesis algorithm for nondeterministic hybrid systems with complex continuous dynamics under temporal and reachability constraints. We model the evolution of the hybrid system as a two-player game, where the nondeterminism is an adversarial player whose objective is to prevent achieving temporal and reachability goals. The aim is to synthesize a winning strategy -- a reactive (robust) strategy that guarantees the satisfaction of the goals under all possible moves of the adversarial player. Our proposed approach involves growing a (search) game-tree in the hybrid space by combining sampling-based motion planning with a novel bandit-based technique to select and improve on partial strategies. We show that the algorithm is probabilistically complete, i.e., the algorithm will asymptotically almost surely find a winning strategy, if one exists. The case studies and benchmark results show that our algorithm is general and effective, and consistently outperforms state of the art algorithms.

Many of the most fundamental laws of nature can be formulated as partial differential equations (PDEs). Understanding these equations is, therefore, of exceptional importance for many branches of modern science and engineering. However, since the general solution of many PDEs is unknown, the efficient approximate solution of these equations is one of humanity's greatest challenges. While multigrid represents one of the most effective methods for solving PDEs numerically, in many cases, the design of an efficient or at least working multigrid solver is an open problem. This thesis demonstrates that grammar-guided genetic programming, an evolutionary program synthesis technique, can discover multigrid methods of unprecedented structure that achieve a high degree of efficiency and generalization. For this purpose, we develop a novel context-free grammar that enables the automated generation of multigrid methods in a symbolically-manipulable formal language, based on which we can apply the same multigrid-based solver to problems of different sizes without having to adapt its internal structure. Treating the automated design of an efficient multigrid method as a program synthesis task allows us to find novel sequences of multigrid operations, including the combination of different smoothing and coarse-grid correction steps on each level of the discretization hierarchy. To prove the feasibility of this approach, we present its implementation in the form of the Python framework EvoStencils, which is freely available as open-source software. This implementation comprises all steps from representing the algorithmic sequence of a multigrid method in the form of a directed acyclic graph of Python objects to its automatic generation and optimization using the capabilities of the code generation framework ExaStencils and the evolutionary computation library DEAP.

Programmers often search for usage examples for API methods. A tool that could generate realistic, idiomatic, and contextual usage examples for one or more APIs would be immensely beneficial to developers. Such a tool would relieve the need for a deep understanding of the API landscape, augment existing documentation, and help discover interactions among APIs. We present CodeScholar, a tool that generates idiomatic code examples demonstrating the common usage of API methods. It includes a novel neural-guided search technique over graphs that grows the query APIs into idiomatic code examples. Our user study demonstrates that in 70% of cases, developers prefer CodeScholar generated examples over state-of-the-art large language models (LLM) like GPT3.5. We quantitatively evaluate 60 single and 25 multi-API queries from 6 popular Python libraries and show that across-the-board CodeScholar generates more realistic, diverse, and concise examples. In addition, we show that CodeScholar not only helps developers but also LLM-powered programming assistants generate correct code in a program synthesis setting.

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the travelling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric travelling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.