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We consider the problem of minimizing the sum of cost functions pertaining to agents over a network whose topology is captured by a directed graph (i.e., asymmetric communication). We cast the problem into the ADMM setting, via a consensus…

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…

We consider the following problem: Given an undirected (mixed) network and a set of ordered source-target, or cause-effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source-target path. This is…

Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…

In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…

Tackling molecular optimization problems using conventional computational methods is challenging, because the determination of the optimized configuration is known to be an NP-hard problem. Recently, there has been increasing interest in…

Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…

We investigate the optimization of graph topologies for quantum sensing networks designed to estimate weak magnetic fields. The sensors are modeled as spin systems governed by a transverse-field Ising Hamiltonian in thermal equilibrium at…

The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…

Graph cuts-based algorithms have achieved great success in energy minimization for many computer vision applications. These algorithms provide approximated solutions for multi-label energy functions via move-making approach. This approach…

The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…

Control theory has seen recently impactful applications in network science, especially in connections with applications in network medicine. A key topic of research is that of finding minimal external interventions that offer control over…

In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…

We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

This work presents a maximum entropy principle based algorithm for solving minimum multiway $k$-cut problem defined over static and dynamic {\em digraphs}. A multiway $k$-cut problem requires partitioning the set of nodes in a graph into…

We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…