Related papers: Tight Lower Bounds for Query Processing on Streami…

In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…

We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…

This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…

As Large Language Models (LLMs) scale to million-token contexts, traditional Mechanistic Interpretability techniques for analyzing attention scale quadratically with context length, demanding terabytes of memory beyond 100,000 tokens. We…

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…

We propose the design and an implementation of a bulk-parallel external memory priority queue to take advantage of both shared-memory parallelism and high external memory transfer speeds to parallel disks. To achieve higher performance by…

When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…

According to Kolmogorov complexity, every finite binary string is compressible to a shortest code -- its information content -- from which it is effectively recoverable. We investigate the extent to which this holds for infinite binary…

Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…

We demonstrate a lower bound technique for linear decision lists, which are decision lists where the queries are arbitrary linear threshold functions. We use this technique to prove an explicit lower bound by showing that any linear…

We study space-pass tradeoffs in graph streaming algorithms for parameter estimation and property testing problems such as estimating the size of maximum matchings and maximum cuts, weight of minimum spanning trees, or testing if a graph is…

In this paper we describe algorithms for computing the BWT and for building (compressed) indexes in external memory. The innovative feature of our algorithms is that they are lightweight in the sense that, for an input of size $n$, they use…

We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…

Longest Increasing Subsequence (LIS) is a fundamental problem in combinatorics and computer science. Previously, there have been numerous works on both upper bounds and lower bounds of the time complexity of computing and approximating LIS,…

We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is…

We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream. The cell probe model is a particularly strong computational model and subsumes, for example, the popular word RAM model.…

Channel symmetry properties that imply the tightness of Shannon's random coding inner bound have recently been used to determine the capacity region of discrete-memoryless two-way channels (DM-TWCs). For channels without such symmetry…

We introduce the poly-streaming model, a generalization of streaming models of computation in which $k$ processors process $k$ data streams containing a total of $N$ items. The algorithm is allowed $O\left(f(k)\cdot M_1\right)$ space, where…

This thesis presents a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for…

Network administrators want to detect TCP-level packet reordering to diagnose performance problems and attacks. However, reordering is expensive to measure, because each packet must be processed relative to the TCP sequence number of its…