Related papers: Local Routing in Sparse and Lightweight Geometric …
We consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces. We show that an $n$-vertex graph embedded on a surface of genus $g$ with at most…
In the online hypergraph matching problem, hyperedges of size $k$ over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A na\"ive greedy algorithm for this…
We initiate the study of degree-bounded network design problems in the online setting. The degree-bounded Steiner tree problem { which asks for a subgraph with minimum degree that connects a given set of vertices { is perhaps one of the…
We present a binary routing tree protocol for distributed hash table overlays. Using this protocol each peer can independently route messages to its parent and two descendants on the fly without any maintenance, global context, and…
In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
We propose a general method for converting online algorithms to local computation algorithms by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We present a new way to visualize a large graph in the style of online geographic maps. The method builds a tile pyramid for semantic zoom: at every zoom level the labels of the highest-ranked nodes remain readable, just as the names of…
We develop a new approach for online network design and obtain improved competitive ratios for several problems. Our approach gives natural deterministic algorithms and simple analyses. At the heart of our work is a novel application of…
Graph embedding is a fundamental problem of mapping nodes of a guest graph into a host graph while minimizing the distance distortion, with broad applications, including virtual network embeddings into physical topologies, VLSI design, or…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic $O(m \log^2 n \log\log^2 n)$ time algorithm. This improves both on the best previously known deterministic running time of $O(m \log^{12}…
This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…
Does there exist O(1)-competitive (self-adjusting) binary search tree (BST) algorithms? This is a well-studied problem. A simple offline BST algorithm GreedyFuture was proposed independently by Lucas and Munro, and they conjectured it to be…
In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…