Related papers: Complexity and Approximation of the Continuous Net…
The concept of Wardrop equilibrium plays an important role in congested traffic problems since its introduction in the early 50's. As shown in [2], when we work in two-dimensional cartesian and increasingly dense networks, passing to the…
The evolution of 5G and Beyond networks has enabled new applications with stringent end-to-end latency requirements, but providing reliable low-latency service with high throughput over public wireless networks is still a significant…
In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging flows are controlled, there exist tight…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…
In the virtual network embedding problem, the goal is to map embed a set of virtual network instances to a given physical network substrate at minimal cost, while respecting the capacity constraints of the physical network. This NP-hard…
In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
The multicommodity capacitated fixed-charge network design problem has been extensively studied in the literature due to its wide range of applications. Despite the fact that many sophisticated solution methods exist today, finding…
We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity…
We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
Multi-access Edge Computing (MEC) facilitates the deployment of critical applications with stringent QoS requirements, latency in particular. This paper considers the problem of jointly planning the availability of computational resources…
The problem of Distance Edge Labeling is a variant of Distance Vertex Labeling (also known as $L_{2,1}$ labeling) that has been studied for more than twenty years and has many applications, such as frequency assignment. The Distance Edge…
Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…
In this paper, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser (1959), we are given a graph $G=(V,E)$ with metric edges costs, a depot…
Resource-constrained project scheduling problems (RCPSP) are at the heart of many production planning problems across a plethora of applications. Although the problem has been studied since the early 1960s, most developments and test…
The zonotope containment problem, i.e., whether one zonotope is contained in another, is a central problem in control theory. Applications include detecting faults and robustifying controllers by computing invariant sets, and obtain fixed…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
In the $k$-edge-connected spanning subgraph ($k$ECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to $k$ link failures: Given an $n$-node $m$-edge graph with a cost function on the edges, our goal…