Related papers: Breaking the Quadratic Barrier: Robust Cardinality…
Accurate cardinality estimates are a key ingredient to achieve optimal query plans. For RDF engines, specifically under common knowledge graph processing workloads, the lack of schema, correlated predicates, and various types of queries…
We present HyperLogLogLog, a practical compression of the HyperLogLog sketch that compresses the sketch from $O(m\log\log n)$ bits down to $m \log_2\log_2\log_2 m + O(m+\log\log n)$ bits for estimating the number of distinct elements~$n$…
Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of…
Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…
Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing…
While quantum computers promise to solve some scientifically and commercially valuable problems thought intractable for classical machines, delivering on this promise will require a large-scale quantum machine. Understanding the impact of…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let $Ext_{\alpha}$ be the class of all connected graphs whose quotient graph obtained from modular…
Graph streams are rapidly evolving sequences of edges that convey continuously changing relationships among entities, playing a crucial role in domains such as networking, finance, and cybersecurity. Their massive scale and high dynamism…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors…
Many real-world matrix datasets arrive as high-throughput vector streams, making it impractical to store or process them in their entirety. To enable real-time analytics under limited computational, memory, and communication resources,…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion. Specifically, we show that for any $\epsilon > 0$,…
Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a…
The key challenge in designing a sketch representation lies with handling the abstract and iconic nature of sketches. Existing work predominantly utilizes either, (i) a pixelative format that treats sketches as natural images employing…