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null (Ed.)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 $(F_0)$ for data streams. Our investigations lead us to observe 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 translation of algorithms developed for $F_0$ estimation to that of model counting, resulting in new algorithms for model counting. We then observe that algorithms in the context of distributed streaming can be transformed to 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 casespecific analysis in prior works. In particular, our view yields a stateofthe art algorithm for multidimensional range efficient $F_0$ estimation with a simpler analysis.more » « less

Lee, James (Ed.)We exhibit several computational problems that are {\em complete} for multipseudodeterministic computations in the following sense: (1) these problems admit $2$pseudodeterministic algorithms (2) if there exists a pseudodeterministic algorithm for any of these problems, then any multivalued function that admits a $k$pseudodeterministic algorithm for a constant $k$, also admits a pseudodeterministic algorithm. We also show that these computational problems are complete for {\em SearchBPP}: a pseudodeterministic algorithm for any of these problems implies a pseudodeterministic algorithm for all problems in SearchBPP.more » « less

Atzmuller, Martin ; Coscia, Michele ; Missaoui, Rokia (Ed.)Influence diffusion has been central to the study of the propagation of information in social networks, where influence is typically modeled as a binary property of entities: influenced or not influenced. We introduce the notion of attitude, which, as described in social psychology, is the degree by which an entity is influenced by the information. We present an information diffusion model that quantifies the degree of influence, i.e., attitude of individuals, in a social network. With this model, we formulate and study the attitude maximization problem. We prove that the function for computing attitude is monotonic and submodular, and the attitude maximization problem is NPHard. We present a greedy algorithm for maximization with an approximation guarantee of $(11/e)$. Using the same model, we also introduce the notion of ``actionable'' attitude with the aim to study the scenarios where attaining individuals with high attitude is objectively more important than maximizing the attitude of the entire network. We show that the function for computing actionable attitude, unlike that for computing attitude, is nonsubmodular but is approximately submodular. We present an approximation algorithm for maximizing actionable attitude in a network. We experimentally evaluated our algorithms and studied empirical properties of the attitude of nodes in the network such as spatial and value distribution of high attitude nodes.more » « less

Pass, Rafael Pass ; Pietrzak, Krzysztof Pietrzak (Ed.)We investigate the complexity of problems that admit perfect zeroknowledge interactive protocols and establish new unconditional upper bounds and oracle separation results. We establish our results by investigating certain {\em distribution testing problems}: computational problems over highdimensional distributions represented by succinct Boolean circuits. A relatively lessinvestigated complexity class $\SBP$ emerged as significant in this study. The main results we establish are: 1. A unconditional inclusion that NIPZK is a subset of CoSBP. 2. Construction of a relativized world in which there is a distribution testing problem that lies in NIPZK but not in SBP, thus giving a relativized separation of NIPZK (and hence PZK) from SBP. 3. Construction of a relativized world in which there is a distribution testing problem that lies in PZK but not in CoSBP, thus giving a relativized separation of PZK from CoSBP.. Results (1) and (3) imply an oracle separating PZK from NIPZK. Our results refine the landscape of perfect zeroknowledge classes in relation to traditional complexity classes.more » « less