PageRank (PR) is a challenging and important network ranking algorithm, which plays a crucial role in information technologies and numerical analysis due to its huge dimension and wide range of possible applications. The traditional approach to PR goes back to the pioneering paper of S. Brin and L. Page, who developed the initial method in … Read more
We provide a simplex algorithm for a structured class of uncapacitated countably-infinite network flow problems. Previous efforts required explicit capacities on arcs with uniformity properties that facilitate duality arguments. By contrast, this paper takes a “primal” approach by devising a simplex method that provably converges to optimal value using arguments based on convergence of spanning … Read more
The aim of Network Design Problem with Vulnerability Constraints (NDPVC), introduced by Gouveia and Leitner [EJOR, 2017], is to design survivable telecommunications networks that impose length bounds on the communication paths of each commodity pair, before and after the failure of any k links. This problem was proposed as an alternative to the Hop-Constrained Survivable … Read more
In this study, we consider the special case of the uncapacitated p-hub center problem, where the weight/flow matrix includes 0 entities. In some real life networks, such as airline networks, cargo networks etc., the zero flow might exist between certain demand points. Typically in airline networks, nobody travels from city i to city i. In … Read more
We study the simultaneous convexification of graphs of bilinear functions that contain bilinear products between variables x and y, where x belongs to a general polytope and y belongs to a simplex. We propose a constructive procedure to obtain a linear description of the convex hull of the resulting set. This procedure can be applied … Read more
Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for {convex} consensus optimization. However, to the behaviors or consensus \emph{nonconvex} optimization, our understanding is more limited. When we lose convexity, we cannot hope our algorithms always return global solutions though they sometimes still do sometimes. Somewhat surprisingly, … Read more
In this work we introduce profit-oriented capacitated ring arborescence problems and present exact and heuristic algorithms. These combinatorial network design problems ask for optimized bi-level networks taking into account arc costs and node profits. Solutions combine circuits on the inner level with arborescences on the outer level of the networks. We consider the prize-collecting, the … Read more
It is widely recognized that early diagnosis of most types of cancers can increase the chances of full recovery or substantially prolong the life of patients. Positron Emission Tomography (PET) has become the standard way to diagnose many types of cancers by generating high quality images of the affected organs. In order to create an … Read more
In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum … Read more
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for … Read more