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In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…
The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…
One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65--110, 1995], also known as the weak structure theorem, revealed the local structure of graphs…
There have been emerging lots of applications for distributed storage systems e.g., those in wireless sensor networks or cloud storage. Since storage nodes in wireless sensor networks have limited battery, it is valuable to find a repair…
A group of mobile agents is given a task to explore an edge-weighted graph $G$, i.e., every vertex of $G$ has to be visited by at least one agent. There is no centralized unit to coordinate their actions, but they can freely communicate…
The inference of minimum spanning arborescences within a set of objects is a general problem which translates into numerous application-specific unsupervised learning tasks. We introduce a unified and generic structure called edit…
In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology…
In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which…
Millions of flows are routed concurrently through a modern data-center. These networks are often built as Clos topologies, and flow demands are constrained only by the link capacities at the ingress and egress points. The minimum congestion…
In optical-processing-enabled network, transitional lightpaths crossing the same node could be optically encoded to each other to achieve greater spectral efficiency. In this context, we present a new research problem, entitled, routing,…
To cope with the ever increasing demand for bandwidth, future wireless networks will be designed with reuse distance equal to one. This scenario requires the implementation of techniques able to manage the strong multiple access…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
In this paper, we study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total original data for each user is proposed, and it is achievable for arbitrary parameters.…
This paper studies the problem of computing quasi-upward planar drawings of bimodal plane digraphs with minimum curve complexity, i.e., drawings such that the maximum number of bends per edge is minimized. We prove that every bimodal plane…
The component size of a graph is the maximum number of edges in any connected component of the graph. Given a graph $G$ and two integers $k$ and $c$, $(k,c)$-Decomposition is the problem of deciding whether $G$ admits an edge partition into…
We consider the problem of decentralized composite optimization over a symmetric connected graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links.…
We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both…
We propose a framework for optimal $t$-matchings excluding the prescribed $t$-factors in bipartite graphs. The proposed framework is a generalization of the nonbipartite matching problem and includes several problems, such as the…