SIAM Journal on Computing

This paper investigates the role of interaction and coins in quantum Arthur--Merlin games (also called public-coin quantum interactive proof systems). While the existing model restricts the messages from the verifier to be classical even in the quantum ...

We prove a characterization of $t$-query quantum algorithms in terms of the unit ball of a space of degree-$(2t)$ polynomials. Based on this, we obtain a refined notion of approximate polynomial degree that equals the quantum query complexity, answering a ...

We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks us to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an invertible ...

We give a fully polynomial-time randomized approximation scheme (FPRAS) for the all-terminal network reliability problem, which is to determine the probability that in an undirected graph, assuming each edge fails independently, the remainder of the graph is ...

We study the possibility of deterministic and randomness-efficient isolation in space-bounded models of computation: Can one efficiently reduce instances of computational problems to equivalent instances that have at most one solution? We present results for ...

For each finite relational structure $A$, let $CSP(A)$ denote the CSP instances whose constraint relations are taken from $A$. The resulting family of problems $CSP(A)$ has been considered heavily in a variety of computational contexts. In this article, we ...

The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical ...

We derive upper and lower bounds on the degree $d$ for which the Lovász $\vartheta$ function, or equivalently sum-of-squares proofs with degree two, can refute the existence of a $k$-coloring in random regular graphs $G_{n,d}$. We show that this type of ...

We prove that any graph excluding $K_r$ as a minor can be partitioned into clusters of diameter at most $\Delta$ while removing at most $O(r/\Delta)$ fraction of the edges. This improves over the results of Fakcharoenphol and Talwar, who, building on the ...