Shay Solomon

Simple deterministic algorithms for fully dynamic maximal matching

A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) n-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that outperforms the naive O(n) one was reported up to this date. The only progress in this direction is due to Ivkovic and Lloyd [14], who in 1993 devised a deterministic algorithm with an amortized update time of O((n+m)√2/2), where m is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of O(√m). Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining (2-ε)-approximate MCM improving upon the naive O(n) was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sub-logarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of O(log n/log log n). This result addresses an open question of Onak and Rubinfeld [19]. We also show a deterministic algorithm with optimal space usage of O(n+m), that for arbitrary graphs maintains a maximal matching with amortized update time of O(√m).

Orienting Fully Dynamic Graphs with Worst-Case Time Bounds

In edge orientations, the goal is usually to orient (direct) the edges of an undirected network (modeled by a graph) such that all out-degrees are bounded. When the network is fully dynamic, i.e., admits edge insertions and deletions, we wish to maintain such an orientation while keeping a tab on the update time. Low out-degree orientations turned out to be a surprisingly useful tool for managing networks.

Balancing Degree, Diameter, and Weight in Euclidean Spanners

In a seminal paper from 1995, Arya et al. [Euclidean spanners: Short, thin, and lanky, in Proceedings of the 27th Annual ACM Symposium on Theory of Computing, ACM, New York, 1995, pp. 489--498] devised a construction that, for any set

Optimality of an algorithm solving the Bottleneck Tower of Hanoi problem

S

Optimal algorithms for tower of hanoi problems with relaxed placement rules

of

Simple Deterministic Algorithms for Fully Dynamic Maximal Matching

n

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

points in

On Optimal Solutions for the Bottleneck Tower of Hanoi Problem

\mathbb R^d

Narrow-Shallow-Low-Light Trees with and without Steiner Points

and any

New Doubling Spanners

\epsilon > 0