Related papers: Mathematical Foundations for Peer-to-Peer Lattice …
The present study proposes a novel collaborative traffic engineering scheme for networks of autonomous systems. Backpressure routing principles are used for deriving priority routing rules that optimally stabilize a network, while…
Classically, planning tasks are studied as a two-step process: plan creation and plan execution. In situations where plan creation is slow (for example, due to expensive information access or complex constraints), a natural speed-up tactic…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
We derive bounds on the path length $\zeta$ of gradient descent (GD) and gradient flow (GF) curves for various classes of smooth convex and nonconvex functions. Among other results, we prove that: (a) if the iterates are linearly convergent…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
Communication latency has become one of the determining factors for the performance of parallel clusters. To design low-latency network topologies for high-performance computing clusters, we optimize the diameters, mean path lengths, and…
We consider an optimization problem posed by an actual newspaper company, which consists of computing a minimum length route for a delivery truck, such that the driver only stops at street crossings, each time delivering copies to all…
This thesis contributes to the theoretical understanding of local update algorithms, especially Local SGD, in distributed and federated optimization under realistic models of data heterogeneity. A central focus is on the bounded…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
In this work, we prove a $\tilde{\Omega}(\lg^{3/2} n )$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with asymmetric linear systems. We use fixed-order GMRES polynomials to approximate $A_\textrm{ff}^{-1}$ and we use these polynomials to build grid…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
We construct integrable realizations of conformal twisted boundary conditions for ^sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with…
We extract a core principle underlying seemingly different fundamental distributed settings, showing sparsity awareness may induce faster algorithms for problems in these settings. To leverage this, we establish a new framework by…
With the rapid development of social network applications, social network has become an important medium for people to interact. For the minimum distance computation of all pairs in networks, Alon N[4] proposed an algorithm with matrix…
Provenance embedding algorithms are well known for tracking the footprints of information flow in wireless networks. Recently, low-latency provenance embedding algorithms have received traction in vehicular networks owing to strict…
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the…
Communication overhead is one of the key challenges that hinders the scalability of distributed optimization algorithms. In this paper, we study local distributed SGD, where data is partitioned among computation nodes, and the computation…