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 ...

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 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 ...

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+\...

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 ...

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 ...

The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lovász [Acta Sci. Math., 42 (1980), ...

For an undirected graph or multigraph $G=(V,E)$ and a function $f:V\to \mathbb{Z_+}$, an $f$-factor is a subgraph whose degree function is $f$. For integral edge weights of maximum magnitude $W$ our algorithm finds a maximum weight $f$-factor in time $\tilde{...

Let $G=(V,E)$ be a weighted graph or multigraph, with $f$ or $b$ a function assigning a nonnegative integer to each vertex. An $f$-factor is a subgraph whose degree function is $f$; a perfect $b$-matching is a $b$-factor in the graph formed from $G$ by ...

We show that variants of spectral sparsification routines can preserve the total spanning tree counts of graphs. By Kirchhoff's matrix-tree theorem, this is equivalent to preserving the determinant of a graph Laplacian minor or, equivalently, of any symmetric ...

In the classical node-disjoint paths (\sf NDP) problem, the input consists of an undirected $n$-vertex graph $G$, and a collection ${\mathcal M}=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand pairs. The goal ...

It is shown that the parity game can be solved in quasi-polynomial time. The parameterized parity game---with $n$ nodes and $m$ distinct values (a.k.a. colors or priorities)---is proven to be in the class of fixed parameter tractable problems when ...

Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866--893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, Bidimensionality: New ...

This paper proves the first superlogarithmic lower bounds on the cell probe complexity of dynamic Boolean (also known as decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for proving ...

One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel algorithms have eluded ...

We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures [B. Allen and I. Munro, J. ACM, 25 (1978), pp. 526--535; D. D. Sleator and R. ...

Let $S$ be a set of $n$ points on a polyhedral terrain $\mathcal{T}$ in $\mathbb{R}^3$, and let $\varepsilon>0$ be a fixed constant. We prove that $S$ admits a $(2+\varepsilon)$-spanner with $O(n\log n)$ edges with respect to the geodesic distance. This is ...