Venkatesan Guruswami, Krzysztof Onak

We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs:

* testing if an undirected graph has a perfect matching (this implies lower bounds for computing a maximum matching or even just the maximum matching size),

* testing if two ... more >>>

Omri Weinstein, David Woodruff

We study $k$-party set disjointness in the simultaneous message-passing model, and show that even if each element $i\in[n]$ is guaranteed to either belong to all $k$ parties or to at most $O(1)$ parties in expectation (and to at most $O(\log n)$ parties with high probability), then $\Omega(n \min(\log 1/\delta, \log ... more >>>

Diptarka Chakraborty, Elazar Goldenberg, Michal Koucky

The Hamming and the edit metrics are two common notions of measuring distances between pairs of strings $x,y$ lying in the Boolean hypercube. The edit distance between $x$ and $y$ is defined as the minimum number of character insertion, deletion, and bit flips needed for converting $x$ into $y$. ...
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Jelani Nelson, Huacheng Yu

We show optimal lower bounds for spanning forest computation in two different models:

* One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole allowed query asks for a spanning forest, which the ... more >>>

Noah Singer, Madhu Sudan, Santhoshini Velusamy

An ordering constraint satisfaction problem (OCSP) is given by a positive integer $k$ and a constraint predicate $\Pi$ mapping permutations on $\{1,\ldots,k\}$ to $\{0,1\}$. Given an instance of OCSP$(\Pi)$ on $n$ variables and $m$ constraints, the goal is to find an ordering of the $n$ variables that maximizes the number ... more >>>

Lijie Chen, Ce Jin, Rahul Santhanam, Ryan Williams

For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the questions: Which lower bounds can be made constructive? What are the consequences ... more >>>

Joanna Boyland, Michael Hwang, Tarun Prasad, Noah Singer, Santhoshini Velusamy

A Boolean maximum constraint satisfaction problem, Max-CSP\((f)\), is specified by a predicate \(f:\{-1,1\}^k\to\{0,1\}\). An \(n\)-variable instance of Max-CSP\((f)\) consists of a list of constraints, each of which applies \(f\) to \(k\) distinct literals drawn from the \(n\) variables. For \(k=2\), Chou, Golovnev, and Velusamy [CGV20, FOCS 2020] obtained explicit ratios ... more >>>