Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for combinatorial algorithm families with multiple parameters.

Abstract--Graph Similarity Computation (GSC) is a fundamental graph-related task where Graph Edit Distance (GED) serves as a prevalent metric. GED is determined by an optimal alignment between a pair of graphs that partitions each into aligned (zero-cost) and unaligned (cost-incurring) substructures. However, the solution for optimal alignment is intractable, motivating Graph Neural Network (GNN)-based GED approximations. Existing GNN-based GED approaches typically learn node embeddings for each graph and then aggregate pairwise node similarities to estimate the final similarity. Despite their effectiveness, we identify a fundamental mismatch between this prevalent node-centric matching paradigm and the core principles of GED. This discrepancy leads to two critical limitations: (1) a failure to capture the global structural correspondence for optimal alignment, and (2) a misattribution of edit costs by learning from spurious node-level signals. T o address these limitations, we propose GCGSim, a GED-consistent graph similarity learning framework that reformulates the GSC task from the perspective of graph-level matching and substructure-level edit costs. Specifically, we make three core technical contributions. First, we design a Graph-Node Cross Matching (GNCM) mechanism to learn pair-aware contextual-ized graph representations. Second, we introduce a principled Prior Similarity-Guided Disentanglement (PSGD) mechanism, justified by variational inference, to unsupervisedly separate graph representations into their aligned and unaligned substructures. Finally, we employ an Intra-Instance Replicate (IIR) consistency regularization to learn a canonical representation for the aligned substructures.

Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for combinatorial algorithm families with multiple parameters.

We present a method to calculate the similarity between words based on their phonetic transcription (their pronunciation) using the Needleman-Wunsch algorithm. We implement this algorithm in Rust and parallelize it on both CPU and GPU to handle large datasets efficiently. The GPU implementation leverages CUDA and the cudarc Rust library to achieve significant performance improvements. We validate our approach by constructing a fully-connected graph where nodes represent words and edges have weights according to the similarity between the words. This graph is then analyzed using clustering algorithms to identify groups of phonetically similar words. Our results demonstrate the feasibility and effectiveness of the proposed method in analyzing the phonetic structure of languages. It might be easily expanded to other languages. This paper is accompanied by a YouTube video and a GitHub repository.

Despite growing interest in process analysis and mining for data-aware specifications, alignment-based conformance checking for declarative process models has focused on pure control-flow specifications, or mild data-aware extensions limited to numerical data and variable-to-constant comparisons. This is not surprising: finding alignments is computationally hard, even more so in the presence of data dependencies. In this paper, we challenge this problem in the case where the reference model is captured using data-aware Declare with general data types and data conditions. We show that, unexpectedly, it is possible to compute data-aware optimal alignments in this rich setting, enjoying at once efficiency and expressiveness. This is achieved by carefully combining the two best-known approaches to deal with control flow and data dependencies when computing alignments, namely A* search and SMT solving. Specifically, we introduce a novel algorithmic technique that efficiently explores the search space, generating descendant states through the application of repair actions aiming at incrementally resolving constraint violations. We prove the correctness of our algorithm and experimentally show its efficiency. The evaluation witnesses that our approach matches or surpasses the performance of the state of the art while also supporting significantly more expressive data dependencies, showcasing its potential to support real-world applications.

Repeated application of the reduction rules to δ is terminating. None of (R1-R3) increases the size of this set again. We prove local confluency for every pair of rules where the left sides overlap. We only inspect moves where there can be overlapping rules, i.e., (R2,R3) and (R2,R2). Canonicity follows from both propositions together with Newman's Lemma [1].

Conformance checking is a fundamental task of process mining, which quantifies the extent to which the observed process executions match a normative process model. The state-of-the-art approaches compute alignments by exploring the state space formed by the synchronous product of the process model and the trace. This often leads to state space explosion, particularly when the model exhibits a high degree of choice and concurrency. Moreover, as alignments inherently impose a sequential structure, they fail to fully represent the concurrent behavior present in many real-world processes. To address these limitations, this paper proposes a new technique for computing partial-order alignments {on the fly using directed Petri net unfoldings, named FoldA. We evaluate our technique on 485 synthetic model-log pairs and compare it against Astar- and Dijkstra-alignments on 13 real-life model-log pairs and 6 benchmark pairs. The results show that our unfolding alignment, although it requires more computation time, generally reduces the number of queued states and provides a more accurate representation of concurrency.

Long event sequences (termed traces) and large data logs that originate from sensors and prediction models are becoming increasingly common in our data-rich world. In such scenarios, conformance checking-validating a data log against an expected system behavior (the process model) can become computationally infeasible due to the exponential complexity of finding an optimal alignment. To alleviate scalability challenges for this task, we propose ConLES, a sliding-window conformance checking approach for long event sequences that preserves the interpretability of alignment-based methods. ConLES partitions traces into manageable subtraces and iteratively aligns each against the expected behavior, leading to significant reduction of the search space while maintaining overall accuracy. We use global information that captures structural properties of both the trace and the process model, enabling informed alignment decisions and discarding unpromising alignments, even if they appear locally optimal. Performance evaluations across multiple datasets highlight that ConLES outperforms the leading optimal and heuristic algorithms for long traces, consistently achieving the optimal or near-optimal solution. Unlike other conformance methods that struggle with long event sequences, ConLES significantly reduces the search space, scales efficiently, and uniquely supports both predefined and discovered process models, making it a viable and leading option for conformance checking of long event sequences.

Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object identities, supporting complex datatypes, handling dependencies among them, and object-aware synchronization. Object-centric Petri nets with identifiers (OPIDs) partially address these needs but treat objects as unstructured identifiers (e.g., order and item IDs), overlooking the rich semantics of complex data values (e.g., item prices or other attributes). To overcome these limitations, we introduce data-aware OPIDs (DOPIDs), a framework that strictly extends OPIDs by incorporating structured data manipulation capabilities, and full synchronization mechanisms. In spite of the expressiveness of the model, we show that it can be made operational: Specifically, we define a novel conformance checking approach leveraging satisfiability modulo theories (SMT) to compute data-aware object-centric alignments.

In many engineering applications, processes must be followed precisely, making conformance checking between event logs and declarative process models crucial for ensuring adherence to desired behaviors. This is a critical area where Artificial Intelligence (AI) plays a pivotal role in driving effective process improvement. However, computing optimal alignments poses significant computational challenges due to the vast search space inherent in these models. Consequently, existing approaches often struggle with scalability and efficiency, limiting their applicability in real-world settings. This paper introduces DeclareAligner, a novel algorithm that uses the A* search algorithm, an established AI pathfinding technique, to tackle the problem from a fresh perspective leveraging the flexibility of declarative models. Key features of DeclareAligner include only performing actions that actively contribute to fixing constraint violations, utilizing a tailored heuristic to navigate towards optimal solutions, and employing early pruning to eliminate unproductive branches, while also streamlining the process through preprocessing and consolidating multiple fixes into unified actions. The proposed method is evaluated using 8,054 synthetic and real-life alignment problems, demonstrating its ability to efficiently compute optimal alignments by significantly outperforming the current state of the art. By enabling process analysts to more effectively identify and understand conformance issues, DeclareAligner has the potential to drive meaningful process improvement and management.