Related papers: On Generalizations of Network Design Problems with…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…
Traditionally, networks such as datacenter interconnects are designed to optimize worst-case performance under arbitrary traffic patterns. Such network designs can however be far from optimal when considering the actual workloads and…
This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…
Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Recently, the method that learns networks layer by layer has attracted increasing interest for its ease of analysis. For the method, the main challenge lies in deriving an optimization target for each layer by inversely propagating the…
This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost…
We consider a quasi two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…
Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…