Preface

It has been a great pleasure for both of us to serve as Guest Coeditors for this Special 50th Anniversary Issue of Networks. As we planned for the special issue, we noted that, during its 50-year existence, Networks has consistently published truly impactful research on network applications, theory, and algorithms. In celebration of the knowledge disseminated by this journal over its history, we wanted to create a special issue that examines major research with roots based in this journal and explores where research in the networks field may grow in the future. The outcome is a set of two special issues by leading researchers in the field. The eight papers appearing in this second of two special issues collectively cover major developments in the field, identify key challenges facing the networks research community, and present new results to kick off ideas for the next half-century of networks research. The Steiner tree problem is one of the most studied problems in combinatorial optimization. Networks has published a large number of articles on the Steiner tree problem, including two surveys, one each in 1987 and 1992. Ljubić [5] starts off this issue with a comprehensive overview of the rich developments on the Steiner tree problem over the last three decades. The paper highlights advances in tools and techniques, with a greater focus on computational advances. It also discusses several novel applications, as well as settings where the Steiner tree problem has been used as a powerful modeling tool, and highlights venues for future research. Network optimization has played a key role in the design and operation of telecommunication networks. However, telecommunication technology has dramatically evolved in an exponential fashion over the past 50 years, carrying ever-increasing amounts of data that society is critically reliant upon to function optimally. Wong [8] takes a forward-looking view at telecommunication technology and highlights network optimization problems and research areas that will be key to the successful design of telecommunication networks of the future. Given our increasing reliance on networks (e.g., data, social, transport, etc.) in our daily lives, network resilience has become a key research area in the networks community. Sharkey et al. [7] explore research pertaining to network resilience theory and applications, particularly regarding how networks return to normal operations after disruptions. This paper clusters network resilience research appearing in the past 50 years into concepts on network robustness, rebound, extensibility, and adaptability. The authors also show where gaps have arisen in the literature and how existing methods might address future problems in this space. The data revolution has impacted how we shop (increasingly online from home) and has profoundly impacted supply chains. In this vein, Archetti and Bertazzi [2] discuss logistics research challenges that have come about as a consequence of e-commerce. Specifically, they focus on Routing and Inventory Routing problems, with an emphasis on routing problems with release dates, routing problems with crowdshipping, and routing problems that are integrated with inventory problems over time. Agatz et al. [1] discuss opportunities for impactful networks research in the transportation and logistics arena. They note that the world and its communities are facing greater and more serious challenges than ever before. Agatz et al. [1] call upon the networks research community to work on a research agenda that addresses some of the most important of these challenges. The agenda they propose is guided by the sustainable development goals outlined by the United Nations and is organized into three areas: (1) well-being, (2) infrastructure, and (3) natural environment. For each area, they identify current and future challenges, as well as research directions to address those challenges. Network flow problems originated as a field in the 1950s and form an important class of optimization problems within the networks community. The maximum flow problem is one of the seminal network flow problems, with applications across a wide variety of domains. Given its wide applicability, it has been well studied, and researchers have focused on developing faster algorithms for it. Orlin and Gong [6] discuss a new variant of an excess scaling algorithm for the maximum flow problem, whose running time is currently the fastest for the maximum flow problem. Barr et al. [3] examine the well-known fixed-charge network flow problem and provide a new heuristic based on a ghost image approach hybridized with tabu search. The ghost image approach generalizes the concept of relaxations and restrictions used in mathematical optimization, while tabu search employs a limited memory to guide optimization of promising search regions. The algorithm not only shows outstanding results for the fixed-cost network problems examined in the paper but also exhibits the potential to effectively address a far greater class of network optimization problems.