In this work, we study the notion of representation obliviousness in the context of pseudodeterministic streaming algorithms. A (randomized) streaming algorithm A is pseudodeterministic, if for every stream D, there is a ''canonical value'' g(D) so that with probability at least 2/3, A on input stream D outputs g(D). Intuitively, a randomized algorithm is representation oblivious if the output distribution of the algorithm does not depend on the representation of the input. We investigate this notion in the context of streaming algorithms, more specifically, distinct elements estimation (F 0 estimation) in data streams. In this context, representation obliviousness captures the idea that the output distribution of an algorithm for estimating F 0 should only depend on the set of distinct elements of the stream. This is a natural notion, as we note that standard streaming algorithms are representation-oblivious in this sense. We prove that any representation oblivious pseudodeterministic streaming algorithm for estimating F 0 must use Ω(n) space, where [n] is the universe. More generally, we prove that any representation oblivious pseudodeterministic t(n)-pass streaming algorithm requires Ω(n/t(n)) space. This lower bound matches the space requirement of the straightforward multi-pass deterministic algorithm that exactly computes F 0 .

In today's digital age, it is becoming increasingly prevalent to retain digital footprints in the cloud indefinitely. Nonetheless, there is a valid argument that entities should have the authority to decide whether their personal data remains within a specific database or is expunged. Indeed, nations across the globe are increasingly enacting legislation to uphold the "Right To Be Forgotten" for individuals. Investigating computational challenges, including the formalization and implementation of this notion, is crucial due to its relevance in the domains of data privacy and management. This work introduces a new streaming model: the 'Right to be Forgotten Data Streaming Model' (RFDS model). The main feature of this model is that any element in the stream has the right to have its history removed from the stream. Formally, the input is a stream of updates of the form (a, Δ) where Δ ∈ {+, ⊥} and a is an element from a universe U. When the update Δ=+ occurs, the frequency of a, denoted as f a , is incremented to f a +1. When the update Δ=⊥, occurs, f a is set to 0. This feature, which represents the forget request, distinguishes the present model from existing data streaming models. This work systematically investigates computational challenges that arise while incorporating the notion of the right to be forgotten. Our initial considerations reveal that even estimating F 1 (sum of the frequencies of elements) of the stream is a non-trivial problem in this model. Based on the initial investigations, we focus on a modified model which we call α-RFDS where we limit the number of forget operations to be at most α fraction. In this modified model, we focus on estimating F 0 (number of distinct elements) and F 1 . We present algorithms and establish almost-matching lower bounds on the space complexity for these computational tasks.

Constraint satisfaction problems (CSPs) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP’s and computation of zeroth frequency moments ( F 0 ) for data streams. Our investigations lead us to observe a striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting and F 0 computation. We design a recipe for translating algorithms developed for F 0 estimation to model counting, resulting in new algorithms for model counting. We also provide a recipe for transforming sampling algorithm over streams to constraint sampling algorithms. We then observe that algorithms in the context of distributed streaming can be transformed into distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framing F 0 estimation as a special case of #DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields an algorithm for multidimensional range efficient F 0 estimation with a simpler analysis.

Given a family of sets (S1, S2,... SM) over a universe Ω, estimating the size of their union in the data streaming model is a fundamental computational problem with a wide variety of applications. The holy grail in the field of streaming is to seek design of algorithms that achieve (ε, δ)-approximation with poly(log |Ω|, ε-1, log δ-1) space and update time complexity.

In this paper we study the problem of estimating the size of the union of sets $S_1, \dots, S_M$ where each set $S_i \subseteq Ømega$ (for some discrete universe $Ømega$) is implicitly presented and comes in a streaming fashion. We define the notion of Delphic sets to capture class of streaming problems where membership, sampling, and counting calls to the sets are efficient. In particular, we show our notion of Delphic sets capture three well known problems: Klee's measure problem (discrete version), test coverage estimation, and model counting of DNF formulas. The Klee's measure problem corresponds to computation of volume of multi-dimension axis aligned rectangles, i.e., every d-dimension axis-aligned rectangle can be defined as $[a_1,b_1] \times [a_2,b_2] \times łdots \times [a_d, b_d]$. The problem of test coverage estimation focuses on the computation of coverage measure for a given testing array in the context of combinatorial testing, which is a fundamental technique in the context of hardware and software testing. Finally, given a DNF formula $\varphi = T_1 \vee T_2 \vee łdots \vee T_M$, the problem of model counting seeks to compute the number of satisfying assignments of $\varphi$. The primary contribution of our work is a simple and efficient sampling-based algorithm, called \hybrid, for estimating the of union of sets in streaming setting. Our algorithm has the space complexity of $O(Rłog |Ømega|)$ and update time is $O(Rłog R \cdot łog(M/δ) \cdot łog|Ømega|)$ where, $R = Ołeft(łog (M/δ)\cdot \varepsilon^2 \right).$ Consequently, our algorithm provides the first algorithm with linear dependence on d for Klee's measure problem in streaming setting for $d>1$, thereby settling the open problem of Tirthpura and Woodruff (PODS-12). Furthermore, a straightforward application of our algorithm lends to an efficient algorithm for coverage estimation problem in streaming setting. We then investigate whether the space complexity for coverage estimation can be further improved, and in this context, we present another streaming algorithm that uses near-optimal $O(tłog n/\varepsilon^2)$ space complexity but uses an update algorithm that is in $\rm P ^\rm NP $, thereby showcasing an interesting time vs space trade-off in the streaming setting. Finally, we demonstrate the generality of our Delphic sets by obtaining a streaming algorithm for model counting of DNF formulas. It is worth remarking that we view a key strength of our work is the simplicity of both the algorithm and its theoretical analysis, which makes it amenable to practical implementation and easy adoption.

Constraint satisfaction problems (CSP's) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP's and computation of zeroth frequency moments F0 for data streams.

We formalize notions of triangle and open-wedge heavy-hitters in large networks. Intuitively, a node of a network G is a triangle heavy-hitter if it participates in relatively many triangles of G (analogously for open wedges). These notions have applications in social network analysis. We consider the triangle and open-wedge heavy-hitter problems: the computational problems of maintaining a set of nodes of a network that participate in many triangles and open wedges. We give sampling-based algorithms for these problems when the input network G comes as an edge stream. We prove theoretical guarantees on the quality of solutions, time and space complexity of these algorithms. This is the first work that studies the triangle and open-wedge heavy hitters problem on massive streaming networks. We evaluate the performance of our proposed algorithms by running on several real-world data sets. These experiments indicate that our algorithms efficiently detect heavy hitters while keeping both the false-positive and the false-negative errors very low.

We study the problem of identifying reactive compound(s) in a solution as efficiently as possible, with the goal of minimizing the number of chemical tests required to make exact identification. The area of group testing is appropriate for this problem, except that most group testing approaches assume that arbitrary tests can be performed, which is not the case in our application. To address this, we introduce a new model called mask-based constrained group testing, develop a randomized algorithm for it, and prove that under the right conditions, the algorithm is guaranteed w.h.p. to efficiently identify the active compounds of a solution with a small number of tests. We also show that our algorithm performs very well empirically on synthetic and real data.