Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each of which offers different levels of dynamism to the user. In this paper, we establish optimal bounds for the final two settings (incremental and dynamic) in the case of a polynomial universe. Our results complete a line of work that has spanned more than two decades, and also come with a surprise: the incremental setting, which has long been viewed as essentially equivalent to the dynamic one, actually has a phase transition, in which, as the value size v approaches log n, the optimal space redundancy actually begins to shrink, going from roughly n log log n (which has long been thought to be optimal) all the way down to Θ(n ) (which is the optimal bound even for the seemingly much-easier value-dynamic setting).

Late Materialization (LM) is a critical technique applied in traditional column stores to speed up analytical queries. However, with modern analytical databases evolved to incorporate a vectorized columnar execution engine, LM's benefits in I/O reduction and fast columnar query processing have diminished. In this paper, we redefine the concept of Late Materialization in the context of modern analytical databases and propose Selective Late Materialization (SLM) to allow each attribute in a query to choose its own materialization point that yields the minimum cost. SLM expands the solution space of the traditional materialization problem from one unified hard-coded binary decision (i.e., early or late) for all attributes to per attribute per query decisions. By integrating SLM into DuckDB, we show that SLM consistently outperforms the baselines of Early Materialization and Late Materialization by 14.7% and 8.9%, respectively, on average using the Join Order Benchmark (JOB), with up to 76.7% latency reduction for individual queries. We observe similar results for the TPC-DS benchmark.

Bipartite graphs are ubiquitous in many domains, e.g., e-commerce platforms, social networks, and academia, by modeling interactions between distinct entity sets. Within these graphs, the butterfly motif, a complete 2×2 biclique, represents the simplest yet significant subgraph structure, crucial for analyzing complex network patterns. Counting the butterflies offers significant benefits across various applications, including community analysis and recommender systems. Additionally, the temporal dimension of bipartite graphs, where edges activate within specific time frames, introduces the concept of historical butterfly counting, i.e., counting butterflies within a given time interval. This temporal analysis sheds light on the dynamics and evolution of network interactions, offering new insights into their mechanisms. Despite its importance, no existing algorithm can efficiently solve the historical butterfly counting task. To address this, we design two novel indices whose memory footprints are dependent on #butterflies and #wedges, respectively. Combining these indices, we propose a graph structure-aware indexing approach that significantly reduces memory usage while preserving exceptional query speed. To further reduce the index size and boost the query efficiency, we design an index compression strategy, enabling the fast, high-quality, and unbiased approximation of historical butterfly counts. We theoretically prove that our approach is particularly advantageous on power-law graphs, a common characteristic of real-world bipartite graphs, by surpassing traditional complexity barriers for general graphs. Extensive experiments reveal that our query algorithms outperform existing methods by up to five magnitudes, effectively balancing speed with manageable memory requirements.

Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced subgraph, crucial for applications like polarized community detection in social networks and portfolio analysis in finance. Traditional models, however, are limited by an assumption of perfect partitioning, which fails to mirror the complexities of real-world data. Addressing this gap, we introduce an innovative generalized balanced subgraph model that incorporates tolerance for imbalance. Our proposed region-based heuristic algorithm, tailored for this NP -hard problem, strikes a balance between low time complexity and high-quality outcomes. Comparative experiments validate its superior performance against leading solutions, delivering enhanced effectiveness (notably larger subgraph sizes) and efficiency (achieving up to 100× speedup) in both traditional and generalized contexts.