Related papers: New Algorithms and Lower Bounds for Streaming Tour…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…
We consider streaming over a peer-to-peer network with homogeneous nodes in which a single source broadcasts a data stream to all the users in the system. Peers are allowed to enter or leave the system (adversarially) arbitrarily. Previous…
Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric…
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…
Recent breakthroughs in graph streaming have led to the design of single-pass semi-streaming algorithms for various graph coloring problems such as $(\Delta+1)$-coloring, degeneracy-coloring, coloring triangle-free graphs, and others. These…
We optimally resolve the space complexity for the problem of finding an $\alpha$-approximate minimum vertex cover ($\alpha$MVC) in dynamic graph streams. We give a randomised algorithm for $\alpha$MVC which uses $O(n^2/\alpha^2)$ bits of…
In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams,…
We consider the corner-stone broadcast task with an adaptive adversary that controls a fixed number of $t$ edges in the input communication graph. In this model, the adversary sees the entire communication in the network and the random…
Graph sketching is a powerful technique introduced by the seminal work of Ahn, Guha and McGregor'12 on connectivity in dynamic graph streams that has enjoyed considerable attention in the literature since then, and has led to near optimal…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
We study graph coloring problems in the streaming model, where the goal is to process an $n$-vertex graph whose edges arrive in a stream, using a limited space that is smaller than the trivial $O(n^2)$ bound. While prior work has largely…
This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F \subseteq E$…
Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-\epsilon)$-approximation for Max-Cut must use $n^{1-O(\epsilon)}$ space; moreover,…
In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal…
This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret…
We prove a hypercontractive inequality for matrix-valued functions defined over large alphabets. In order to do so, we prove a generalization of the powerful $2$-uniform convexity inequality for trace norms of Ball, Carlen, Lieb…
While there are software systems that simplify trajectory streams on the fly, few curve simplification algorithms with quality guarantees fit the streaming requirements. We present streaming algorithms for two such problems under the…
In recent years, the problem of computing the frequencies of the induced $k$-vertex subgraphs of a graph, or \emph{$k$-graphlets}, has become central. One approach for this problem is to sample $k$-graphlets randomly. Classic algorithms for…
The degree distribution of a graph $G=(V,E)$, $|V|=n$, $|E|=m$ is one of the most fundamental objects of study in the analysis of graphs as it embodies relationship among entities. In particular, an important derived distribution from…