SIAM Journal on Computing

Let $\pi$ be an efficient two-party protocol that, given security parameter $\kappa$, both parties output single bits $X_\kappa$ and $Y_\kappa$, respectively. We are interested in how $(X_\kappa,Y_\kappa)$ “appears” to an efficient adversary that only ...

The Restricted Assignment problem is a prominent special case of Scheduling on Unrelated Parallel Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the nonconstructive bound on its integrality gap from 1.9412 to ...

In 2015, Guth [Math. Proc. Cambridge Philos. Soc., 159 (2015), pp. 459--469] proved that for any set of $k$-dimensional bounded complexity varieties in ${\mathbb R}^d$ and for any positive integer $D$, there exists a polynomial of degree at most $D$ whose ...

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g., via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially ...

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, ...

In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: “strict” and “weak,” and in the associated decision problem one must distinguish between being ...

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family $\mathcal{B} \subseteq 2^{[m]}$, find a set $S \in \mathcal{B}$ that maximizes the ...

We consider a set of transmitters broadcasting simultaneously on the same frequency under the signal to interference plus noise ratio (SINR) model. Transmission power may vary from one transmitter to another, and a transmitter's signal strength at a given ...

We give an algorithmic and lower bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding algorithms with ...

We examine the problem of determining whether a multiqubit two-local Hamiltonian can be made stoquastic by single-qubit unitary transformations. We prove that when such a Hamiltonian contains one-local terms, then this task can be NP-hard. This is shown ...

We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_\star$ failed vertices in $\tilde{O}(d^3)$ time and thereafter answers connectivity ...

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 note indicates an error in the proof of Theorem 3.1 in [T. Vidick, SIAM J. Comput., 45 (2016), pp. 1007--1063]. Due to an induction step in the soundness analysis not being carried out correctly, the analysis fails to prove the claimed result. The ...