Related papers: A Novel Mathematical Model for the Unique Shortest…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
This work addresses the problem of evaluating optimal link capacities of a packet-flow network for the objective of congestion minimization. We present a simple model of packet flow in networks and present a numerical approach to evaluate…
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
In operational networks, nodes are connected via multiple links for load sharing and redundancy. This is done to make sure that a failure of a link does not disconnect or isolate some parts of the network. However, link failures have an…
In this paper, we investigate a novel minimum length scheduling problem to determine the optimal power control, and scheduling for constant and continuous rate models, while considering concurrent transmission of users, energy causality,…
For $s$ $>$ 0, we consider an algorithm that computes all $s$-well separated pairs in certain point sets in $\mathbb{R}^{n}$, $n$ $>1$. For an integer $K$ $>1$, we also consider an algorithm that is a permutation of Dijkstra's algorithm,…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
The shortest path problem is a typical problem in graph theory with wide potential applications. The state-of-the-art single-source shortest paths algorithm on the weight graph is the $\Delta$-stepping algorithm, which can efficiently…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…
The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
Backpressure-based adaptive routing algorithms where each packet is routed along a possibly different path have been extensively studied in the literature. However, such algorithms typically result in poor delay performance and involve high…
We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional ($d=2$) square lattices to be improved by the…
We study the problem of computing constrained shortest paths for battery electric vehicles. Since battery capacities are limited, fastest routes are often infeasible. Instead, users are interested in fast routes on which the energy…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…