While research on the geometry of planar graphs has been active in the past decades, many
properties of planar metrics remain mysterious. This paper studies a fundamental aspect of …

In the LOCAL model of distributed computing, low-diameter decomposition is an extremely
useful tool in designing algorithms, as it allows us to shift from the general graph setting to …

This article proves strong lower bounds for distributed computing in the congest model, by
presenting the bit-gadget: a new technique for constructing graphs with small cuts. The …

Under the Strong Exponential-Time Hypothesis, the diameter of general unweighted graphs
cannot be computed in truly subquadratic time. Nevertheless there are several graph …

Many combinatorial optimization problems, including maximum weighted matching and
maximum independent set, can be approximated within (1±ε) factors in poly (log n, 1/ε) …

We prove that any n-node graph G with diameter D admits shortcuts with congestion O (δ D
log n) and dilation O (δ D), where δ is the maximum edge-density of any minor of G. Our …

Under the strong exponential-time hypothesis, the diameter of general unweighted graphs
cannot be computed in truly subquadratic time (in the size of the input), as shown by Roditty …

We extract a core principle that underlies seemingly different fundamental distributed
settings, which is that sparsity awareness may induce faster algorithms for core problems in …

Reidl et al.(Eur J Comb 75: 152–168, 2019) characterized graph classes of bounded
expansion as follows: A class C closed under subgraphs has bounded expansion if and only …

Spanners for metric spaces have been extensively studied, perhaps most notably in low-
dimensional Euclidean spaces-due to their numerous applications. Euclidean spanners can …