This issue of SICOMP contains six specially selected papers from STOC 2020, the Fifty-second Annual ACM Symposium on the Theory of Computing, which was held June 22--26, 2020, initially planned at Chicago, Illinois, but due to COVID-19 was an online ...

This issue of SICOMP contains ten specially selected papers from STOC 2017, the Forty-ninth Annual ACM Symposium on the Theory of Computing, which was held June 19--23 in Montreal, Canada. The papers here were chosen to represent the range and quality of the ...

We provide several advances to the understanding of the class of quantum Merlin--Arthur (QMA) proof systems, the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the consistency of local density matrices (CLDM) ...

We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and Végh [J. ACM, 67 (2020), 37]. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus ...

We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from the interior of polytopes in $\mathbb{R}^{n}$ specified by $m$ inequalities. The walk is a discrete-time simulation of a ...

We provide the first separation in the approximation guarantee achievable by truthful and nontruthful algorithms for combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\nicefrac{3}{4}-\...

We present a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $\Delta$ and an integer $k > 3\Delta$ and returns a random proper $k$-coloring of $G$. The distribution of the coloring is perfectly uniform over ...

In a recent breakthrough, [C. Murray and R. R. Williams, STOC 2018, ACM, New York, 2018, pp. 890--901] proved that ${NQP} = {NTIME}[n^{{polylog}(n)}]$ cannot be computed by polynomial-size ${ACC}^0$ circuits (constant-depth circuits consisting of ${AND}$/...

For positive integers $U$, $n$, and $\sigma$, given a set $S$ of $n$ (distinct) keys from key space $[U]$, each associated with a value from $[\sigma]$, the static dictionary problem asks one to preprocess these (key, value) pairs into a data structure, ...

We present a black-box reduction from the path version of the traveling salesman problem (Path TSP) to the classical tour version (TSP). More precisely, given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon >0$, we obtain an $(\alpha+\...

This paper considers a special class of nonlocal games $(G,\psi)$, where $G$ is a two-player one-round game, and $\psi$ is a bipartite state independent of $G$. In the game $(G,\psi)$, the players are allowed to share arbitrarily many copies of $\psi$. The ...

For every constant $d \geq 3$ and $\epsilon > 0$, we give a deterministic $\operatorname{poly}(n)$-time algorithm that outputs a $d$-regular graph on $\Theta(n)$ vertices that is $\eps$-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by $2\...

We consider the pattern detection problem in graphs: given a constant size pattern graph $H$ and a host graph $G$, determine whether $G$ contains a subgraph isomorphic to $H$. We present the following new improved upper and lower bounds: We prove that if a ...

This corrigendum corrects errors found by Jérémie Dusart in the proof of correctness of the algorithms in [D. G. Corneil, B. Dalton, and M. Habib, SIAM J. Comput., 42 (2013), pp. 792--807]; there are no changes in the algorithms themselves.

We initiate the study of computing (near-)optimal contracts in succinctly representable principal-agent settings. Here optimality means maximizing the principal's expected payoff over all incentive-compatible contracts---known in economics as “second-best” ...

We present a spectral analysis of a continuous scaling algorithm for matrix scaling and operator scaling. The main result is that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a ...

We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an $\alpha$-approximation ...

In the 1970s, Lovász built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings [Proceedings of FCT, 1979, pp. 565--574]. A similar connection between bipartite graphs and matrix spaces plays a key role in the recent ...

In this paper, we prove the first fixed-depth size-hierarchy theorem for uniform ${\mathrm{AC}}^0[\oplus]$. In particular, we show that for any fixed $d$ and integer parameter $k$, the class ${\mathcal{{C}}}_{d,k}$ of functions that have uniform ${\mathrm{AC}...

We show that for constraint satisfaction problems (CSPs), weakly exponential size linear programming relaxations are as powerful as the explicit linear program described by $n^{\Omega(1)}$-rounds of the Sherali--Adams linear programming hierarchy. ...