Related papers: The space complexity of recognizing well-parenthes…
Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
Frequency estimation in data streams is one of the classical problems in streaming algorithms. Following much research, there are now almost matching upper and lower bounds for the trade-off needed between the number of samples and the…
We prove that any semi-streaming algorithm for $(1-\epsilon)$-approximation of maximum bipartite matching requires \[ \Omega(\frac{\log{(1/\epsilon)}}{{\log{(1/\beta)}}}) \] passes, where $\beta \in (0,1)$ is the largest parameter so that…
We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, we…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Storing a counter incremented $N$ times would naively consume $O(\log N)$ bits of memory. In 1978 Morris described the very first streaming algorithm: the "Morris Counter". His algorithm's space bound is a random variable, and it has been…
We show a lower bound on expected communication cost of interactive entanglement assisted quantum state redistribution protocols and a slightly better lower bound for its special case, quantum state transfer. Our bound implies that the…
In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages…
We study the power of Arthur-Merlin probabilistic proof systems in the data stream model. We show a canonical $\mathcal{AM}$ streaming algorithm for a wide class of data stream problems. The algorithm offers a tradeoff between the length of…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…
This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also…
Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…
We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…
Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming…
The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges.…
In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with…