Related papers: Box Covers and Domain Orderings for Beyond Worst-C…
We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is…
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice.…
Worst-case optimal join algorithms are the class of join algorithms whose runtime match the worst-case output size of a given join query. While the first provably worst-case optimal join algorithm was discovered relatively recently, the…
Efficient join processing is one of the most fundamental and well-studied tasks in database research. In this work, we examine algorithms for natural join queries over many relations and describe a novel algorithm to process these queries…
Relatively recently, the field of join processing has been swayed by the discovery of a new class of multi-way join algorithms. The new algorithms join multiple relations simultaneously rather than perform a series of pairwise joins. The…
Worst-case optimal join algorithms have so far been studied in two broad contexts -- $(1)$ when we are given input relation sizes [Atserias et al., FOCS 2008, Ngo et al., PODS 2012, Velduizhen et. al, ICDT 2014] $(2)$ when in addition to…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
We study the problem of optimizing subgraph queries using the new worst-case optimal join plans. Worst-case optimal plans evaluate queries by matching one query vertex at a time using multiway intersections. The core problem in optimizing…
Two central problems in Stochastic Optimization are Min Sum Set Cover and Pandora's Box. In Pandora's Box, we are presented with $n$ boxes, each containing an unknown value and the goal is to open the boxes in some order to minimize the sum…
The box-constrained integer least squares problem (BILS) arises in MIMO wireless communications applications. Typically a sphere decoding algorithm (a tree search algorithm) is used to solve the problem. In order to make the search…
We present an elementary branch and bound algorithm with a simple analysis of why it achieves worstcase optimality for join queries on classes of databases defined respectively by cardinality or acyclic degree constraints. We then show that…
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have…
In the last few years, much effort has been devoted to developing join algorithms in order to achieve worst-case optimality for join queries over relational databases. Towards this end, the database community has had considerable success in…
We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows.…
Grover's algorithm searches for data satisfying a desired condition in an unstructured database. This algorithm can search a space of size $N$ in $\sqrt{N}$ queries, thereby achieving a quadratic speedup. However, within the Grover oracle…
Join order optimization is among the most crucial query optimization problems, and its central position is also evident in the new research field where quantum computing is applied to database optimization and data management. In the field,…
Significant research effort has been devoted to improving the performance of join processing in the massively parallel computation model, where the goal is to evaluate a query with the minimum possible data transfer between machines.…
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in $(0,1]$, and a partition matroid over the items. The goal is to pack all items in a minimum number of unit-size bins, such that…
Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most…