Kidney Exchange: Faster Parameterized Algorithms and Tighter Lower Bounds

The kidney exchange mechanism allows many patient-donor pairs who are otherwise incompatible with each other to come together and exchange kidneys along a cycle. However, due to infrastructure and legal constraints, kidney exchange can only be performed in small cycles in practice. In reality, there are also some altruistic donors who do not have any paired patients. This allows us to also perform kidney exchange along paths that start from some altruistic donor. Unfortunately, the computational task is NP-complete. To overcome this computational barrier, an important line of research focuses on designing faster algorithms, both exact and using the framework of parameterized complexity. The standard parameter for the kidney exchange problem is the number $t$ of patients that receive a healthy kidney. The current fastest known deterministic FPT algorithm for this problem, parameterized by $t$, is $O^\star\left(14^t\right)$. In this work, we improve this by presenting a deterministic FPT algorithm that runs in time $O^\star\left((4e)^t\right)\approx O^\star\left(10.88^t\right)$. This problem is also known to be W[1]-hard parameterized by the treewidth of the underlying undirected graph. A natural question here is whether the kidney exchange problem admits an FPT algorithm parameterized by the pathwidth of the underlying undirected graph. We answer this negatively in this paper by proving that this problem is W[1]-hard parameterized by the pathwidth of the underlying undirected graph. We also present some parameterized intractability results improving the current understanding of the problem under the framework of parameterized complexity.

Cost-Effective, Low Latency Vector Search with Azure Cosmos DB

Vector indexing enables semantic search over diverse corpora and has become an important interface to databases for both users and AI agents. Efficient vector search requires deep optimizations in database systems. This has motivated a new class of specialized vector databases that optimize for vector search quality and cost. Instead, we argue that a scalable, high-performance, and cost-efficient vector search system can be built inside a cloud-native operational database like Azure Cosmos DB while leveraging the benefits of a distributed database such as high availability, durability, and scale. We do this by deeply integrating DiskANN, a state-of-the-art vector indexing library, inside Azure Cosmos DB NoSQL. This system uses a single vector index per partition stored in existing index trees, and kept in sync with underlying data. It supports < 20ms query latency over an index spanning 10 million of vectors, has stable recall over updates, and offers nearly 15x and 41x lower query cost compared to Zilliz and Pinecone serverless enterprise products. It also scales out to billions of vectors via automatic partitioning. This convergent design presents a point in favor of integrating vector indices into operational databases in the context of recent debates on specialized vector databases, and offers a template for vector indexing in other databases.

An Automated Machine Learning Approach to Inkjet Printed Component Analysis: A Step Toward Smart Additive Manufacturing

In this paper, we present a machine learning based architecture for microwave characterization of inkjet printed components on flexible substrates. Our proposed architecture uses several machine learning algorithms and automatically selects the best algorithm to extract the material parameters (ink conductivity and dielectric properties) from on-wafer measurements. Initially, the mutual dependence between material parameters of the inkjet printed coplanar waveguides (CPWs) and EM-simulated propagation constants is utilized to train the machine learning models. Next, these machine learning models along with measured propagation constants are used to extract the ink conductivity and dielectric properties of the test prototypes. To demonstrate the applicability of our proposed approach, we compare and contrast four heuristic based machine learning models. It is shown that eXtreme Gradient Boosted Trees Regressor (XGB) and Light Gradient Boosting (LGB) algorithms perform best for the characterization problem under study.