SIAM Journal on Computing

Local Versus Global Properties of Metric Spaces

Sanjeev Arora, Laszlo Lovasz, Ilan Newman, Yuval Rabani, Yuri Rabinovich et al.
Motivated by applications in combinatorial optimization, we study the extent to which the global properties of a metric space, and especially its embeddability into $\ell_1$ with low distortion, are determined by the properties of its small subspaces. We establish both upper and lower bounds on the ... [SIAM J. Comput. 41, 250 (2012)] published Thu Feb 9, 2012.

Explicit Dimension Reduction and Its Applications

Zohar S. Karnin, Yuval Rabani, and Amir Shpilka
We construct a small set of explicit linear transformations mapping $\mathbb{R}^n$ to $\mathbb{R}^t$, where $t=O(\log (\gamma^{-1}) \epsilon^{-2})$, such that the $L_2$ norm of any vector in $\mathbb{R}^n$ is distorted by at most $1\pm \epsilon$ in at least a fraction of $1 - \gamma$ of the transfo ... [SIAM J. Comput. 41, 219 (2012)] published Thu Feb 2, 2012.

The Complexity of Distributions

Emanuele Viola
Complexity theory typically studies the complexity of computing a function $h(x) : \{0, 1\}^m \to \{0, 1\}^n$ of a given input $x$. A few works have suggested studying the complexity of generatingor samplingthe distribution $h(x)$ for uniform $x$, given random bits. We further advocate this study, ... [SIAM J. Comput. 41, 191 (2012)] published Thu Feb 2, 2012.

Regular Expressions with Counting: Weak versus Strong Determinism

Wouter Gelade, Marc Gyssens, and Wim Martens
We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which are equally expressive for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show ... [SIAM J. Comput. 41, 160 (2012)] published Tue Jan 31, 2012.

Exponential Lower Bounds and Integrality Gaps for Tree-Like LovaszSchrijver Procedures

Toniann Pitassi and Nathan Segerlind
The matrix cuts of Lovasz and Schrijver are methods for tightening linear relaxations of zero-one programs by the addition of new linear inequalities. We address the question of how many new inequalities are necessary to approximate certain combinatorial problems, and we solve certain instances of ... [SIAM J. Comput. 41, 128 (2012)] published Tue Jan 31, 2012.

Iterated Rounding Algorithms for the Smallest k-Edge Connected Spanning Subgraph

Harold N. Gabow and Suzanne R. Gallagher
We present the best known algorithms for approximating the minimum-size undirected $k$-edge connected spanning subgraph. For simple graphs our approximation ratio is $1+ {1}/(2k) + O({1}/{k^2})$. The more precise version of this bound requires $k\ge 7$, and for all such $k$ it improves the long-sta ... [SIAM J. Comput. 41, 61 (2012)] published Tue Jan 24, 2012.

An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries

Pankaj K. Agarwal, Lars Arge, Haim Kaplan, Eyal Molad, Robert E. Tarjan et al.
Let $S$ be a set of $n$ intervals in $\mathbb{R}$, and let $(\mathbf{S}, +)$ be any commutative semigroup. We assign a weight $\omega(s) \in \mathbf{S}$ to each interval in $S$. For a point $x \in \mathbb{R}$, let $S(x) \subseteq S$ be the set of intervals that contain $x$. Given a point $q \in \ma ... [SIAM J. Comput. 41, 104 (2012)] published Tue Jan 24, 2012.

On Clustering to Minimize the Sum of Radii

Matt Gibson, Gaurav Kanade, Erik Krohn, Imran A. Pirwani, and Kasturi Varadarajan
Let $P$ be a set of $n$ points in the plane. Consider the problem of finding $k$ disks, each centered at a point in $P$, whose union covers $P$ with the objective of minimizing the sum of the radii of the disks. We present an exact algorithm for this well-studied problem with polynomial running tim ... [SIAM J. Comput. 41, 47 (2012)] published Thu Jan 5, 2012.

The Gathering Problem for Two Oblivious Robots with Unreliable Compasses

Taisuke Izumi, Samia Souissi, Yoshiaki Katayama, Nobuhiro Inuzuka, Xavier Defago et al.
Anonymous mobile robots are often classified into synchronous, semi-synchronous, and asynchronous robots when discussing the pattern formation problem. For semi-synchronous robots, all patterns formable with memory are also formable without memory, with the single exception of forming a point (i.e. ... [SIAM J. Comput. 41, 26 (2012)] published Tue Jan 3, 2012.

Envy-Free Makespan Approximation

Edith Cohen, Michal Feldman, Amos Fiat, Haim Kaplan, and Svetlana Olonetsky
We study envy-free mechanisms for assigning tasks to agents, where every task may take a different amount of time to perform by each agent, and the goal is to get all the tasks done as soon as possible (i.e., minimize the makespan). For indivisible tasks, we put forward an envy-free polynomial mech ... [SIAM J. Comput. 41, 12 (2012)] published Tue Jan 3, 2012.