For any >0, we give a simple, deterministic (4+)-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. The previous best approximation factor was 380 via a randomized algorithm. We also consider the asymmetric ...

We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory ‍V₂⁰ is consistent with the conjecture that ‍NEXP ‍⊈ ‍P/poly, i.e., ...

We study sublinear time algorithms for estimating the size of maximum matching. After a long line of research, the problem was finally settled by Behnezhad ‍[FOCS’22], in the regime where one is willing to pay an approximation factor of 2. Very recently, ...

An f-edge fault-tolerant distance sensitive oracle (f-DSO) with stretch σ ≥ 1 is a data structure that preprocesses a given undirected, unweighted graph G with n vertices and m edges, and a positive integer f. When queried with a pair of vertices s, t ...

The group isomorphism problem determines whether two groups, given by their Cayley tables, are isomorphic. For groups with order n, an algorithm with n^{(logn + O(1))} running time, attributed to Tarjan, was proposed in the 1970s (Miller, STOC 1978). ...

Kol and Raz [STOC 2013] showed how to simulate any alternating two-party communication protocol designed to work over the noiseless channel, by a protocol that works over a stochastic channel that corrupts each sent symbol with probability ‍є>0 ...

Quantum entanglement is a fundamental property of quantum mechanics and it serves as a basic resource in quantum computation and information. Despite its importance, the power and limitations of quantum entanglement are far from being fully ...

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic guarantees. Naturally, ...

The notion of replicable algorithms was introduced by Impagliazzo, Lei, Pitassi, and Sorrell (STOC’22) to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output ...

We give an algorithm that takes as input an n-vertex graph G and an integer k, runs in time 2^O(k2) n^O(1), and outputs a tree decomposition of G of width at most k, if such a decomposition exists. This resolves the long-standing open problem of whether ...

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of P, such as depth-...

We present an Õ(log² n) round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching, Δ+1 vertex coloring, and 2Δ−1 edge coloring. These four problems ...

We analyse uniformly random proper k-colourings of sparse graphs with maximum degree Δ in the regime Δ < klnk . This regime corresponds to the lower side of the shattering threshold for random graph colouring, a paradigmatic example of the shattering ...

We study the concurrent composition properties of interactive differentially private mechanisms, whereby an adversary can arbitrarily interleave its queries to the different mechanisms. We prove that all composition theorems for non-interactive ...

The “short cycle removal” technique was recently introduced by Abboud, Bringmann, Khoury and Zamir (STOC ’22) to prove fine-grained hardness of approximation. Its main technical result is that listing all triangles in an n^1/2-regular graph is n^2−o(1)-...

In this paper we provide a new locally consistent decomposition of strings. Each string x is decomposed into blocks that can be described by grammars of size O(k) (using some amount of randomness). If we take two strings x and y of edit distance at ...

The δ-Coin Problem is the problem of distinguishing between a sequence of coin tosses that come up Heads with probability either 1+δ/2 or 1−δ/2. The computational complexity of this problem in various models has been studied in many previous works ...

In this paper we carefully combine Fredman’s trick [SICOMP’76] and Matoušek’s approach for dominance product [IPL’91] to obtain powerful results in fine-grained complexity.

Under the hypothesis that APSP for undirected graphs with edge weights in {1, ...

Cut games are among the most fundamental strategic games in algorithmic game theory. It is well-known that computing an exact pure Nash equilibrium in these games is PLS-hard, so research has focused on computing approximate equilibria. We present a ...

This paper introduces stronger notions for approximate single-source shortest-path distances and gives simple reductions to compute them from weaker standard notions of approximate distances. Strongly-approximate distances isolate, capture, and ...