SIAM Journal on Computing

We establish the first polynomial-strength time-space lower bounds for problems in the linear-time hierarchy on randomized machines with two-sided error. We show that for any integer $\ell > 1$ and constant $c < \ell$, there exists a positive constant $...

A set $A$ is autoreducible if one can compute, for all $x$, the value $A(x)$ by querying $A$ only at places $y \neq x$. Furthermore, $A$ is infinitely-often autoreducible if, for infinitely many $x$, the value $A(x)$ can be computed by querying $A$ only ...

The Lova´sz local lemma due to Erdo˝s and Lova´sz (Infinite and Finite Sets, Colloq. Math. Soc. J. Bolyai 11, 1975, pp. 609-627) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the ...

Jackson and Wormald conjecture that if $G$ is a 3-connected $n$-vertex graph with maximum degree $d\ge 4$, then $G$ has a cycle of length $\Omega(n^{\log_{d-1}2})$. We show that this conjecture holds when $d-1$ is replaced by $\max\{64,4d+1\}$. Our ...

In many optimization problems, one seeks to allocate a limited set of resources to a set of individuals with demands. Thus, such allocations can naturally be viewed as vectors, with one coordinate representing each individual. Motivated by work in ...

Inspired by dynamic connectivity applications in computational geometry, we consider a problem we call dynamic subgraph connectivity: design a data structure for an undirected graph $G=(V,E)$ and a subset of vertices $S \subseteq V$ to support ...

We show that a set of $n$ points in the plane has at most $O(10.05^n)$ perfect matchings with crossing-free straight-line embedding. The expected number of perfect crossing-free matchings of a set of $n$ points drawn independently and identically ...

We present an algorithm to enumerate the pointed pseudotriangulations of a given point set, based on the greedy flip algorithm of Pocchiola and Vegter [Discrete Comput. Geom. 16 (1996), pp. 419-453]. Our two independent implementations agree and allow ...

Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds on the location ...

Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structures of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift ...

In this work we fill the knowledge gap concerning testing polynomials over finite fields. As previous works show, when the cardinality of the field, $q$, is sufficiently larger than the degree bound, $d$, then the number of queries sufficient for ...

In [S. Safra, Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988, pp. 319-327] an exponential determinization procedure for Buchi automata was shown, yielding tight bounds for decision procedures of some logics (see [A. E. ...

Let $S$ be a set of $n$ points in $\reals^2$. Given an integer $1 \le k \le n$, we wish to find a maximally separated subset $I \subseteq S$ of size $k$; this is a subset for which the minimum among the ${k\choose 2}$ pairwise distances between its ...

Let ${\mathcal R}(n,k)$ denote the random $k$-ary relation defined on the set $[n]=\{1,2,\dots,n\}$. We show that the probability that $([n], {\mathcal R}(n,k))$ is projective tends to one, as either $n$ or $k$ tends to infinity. This result implies ...