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We show that every labelled planar graph $G$ can be assigned a canonical embedding $\phi(G)$, such that for any planar $G'$ that differs from $G$ by the insertion or deletion of one edge, the number of local changes to the combinatorial…
We give a fully dynamic deterministic algorithm for maintaining a maximal matching of an $n$-vertex graph in $\tilde{O}(n^{8/9})$ amortized update time. This breaks the long-standing $\Omega(n)$-update-time barrier on dense graphs,…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
We consider a dynamic model for competition in a social network, where two strategic agents have fixed beliefs and the non-strategic/regular agents adjust their states according to a distributed consensus protocol. We suppose that one…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
The performance of many large-scale and data-intensive distributed systems critically depends on the capacity of the interconnecting network. This paper is motivated by the vision of self-adjusting infrastructures whose resources can be…
In this paper we show how to find nearly optimal embeddings of large trees in several natural classes of graphs. The size of the tree T can be as large as a constant fraction of the size of the graph G, and the maximum degree of T can be…
We provide a deterministic scheme for solving any decidable problem in the distributed {sleeping model}. The sleeping model is a generalization of the standard message-passing model, with an additional capability of network nodes to enter a…
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…
For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a…
A fundamental problem in wireless networks is the \emph{minimum spanning tree} (MST) problem: given a set $V$ of wireless nodes, compute a spanning tree $T$, so that the total cost of $T$ is minimized. In recent years, there has been a lot…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
In low distortion metric embeddings, the goal is to embed a host "hard" metric space into a "simpler" target space while approximately preserving pairwise distances. A highly desirable target space is that of a tree metric. Unfortunately,…
In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…
We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…