Related papers: SPHERE: Spherical partitioning for large-scale rou…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work…
Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Hypergraph partitioning is an NP-hard problem that occurs in many computer science applications where it is necessary to reduce large problems into a number of smaller, computationally tractable sub-problems. Current techniques use a…
We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We describe a method to subdivide the surface of a sphere into spherical triangles of similar, but not identical, shapes and sizes. The Hierarchical Triangular Mesh (HTM) is a quad-tree that is particularly good at supporting searches at…
The balanced hypergraph partitioning problem is to partition a hypergraph into $k$ disjoint blocks of bounded size such that the sum of the number of blocks connected by each hyperedge is minimized. We present an improvement to the…
To overcome the physical limitations of scaling monolithic quantum computers, distributed quantum computing (DQC) interconnects multiple smaller-scale quantum processing units (QPUs) to form a quantum network. However, this approach…
Answering exact shortest path distance queries is a fundamental task in graph theory. Despite a tremendous amount of research on the subject, there is still no satisfactory solution that can scale to billion-scale complex networks.…