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TR21-027 | 24th February 2021
Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena, Zhao Song, Huacheng Yu

#### Almost Optimal Super-Constant-Pass Streaming Lower Bounds for Reachability

We give an almost quadratic $n^{2-o(1)}$ lower bound on the space consumption of any $o(\sqrt{\log n})$-pass streaming algorithm solving the (directed) $s$-$t$ reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including ... more >>>

TR21-026 | 23rd February 2021
Joshua Brakensiek, Venkatesan Guruswami, Sai Sandeep

#### Conditional Dichotomy of Boolean Ordered Promise CSPs

Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form can be satisfied vs. even the weak form cannot be satisfied. Since their ... more >>>

TR21-025 | 15th February 2021
Sivakanth Gopi, Venkatesan Guruswami

#### Improved Maximally Recoverable LRCs using Skew Polynomials

An $(n,r,h,a,q)$-Local Reconstruction Code is a linear code over $\mathbb{F}_q$ of length $n$, whose codeword symbols are partitioned into $n/r$ local groups each of size $r$. Each local group satisfies $a$' local parity checks to recover from $a$' erasures in that local group and there are further $h$ global parity ... more >>>

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