Tangle bases: Revisited

Hicks, Illya V.; Brimkov, Boris

doi:10.1002/net.21979

Cited by 2 publications

(2 citation statements)

References 67 publications

(113 reference statements)

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“…The investigation of graph width parameters finds extensive applications across diverse fields, such as matroid theory, lattice theory, theoretical computer science, game theory, network theory, artificial intelligence, graph theory, and discrete mathematics, as evidenced by numerous studies (for example, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]22,[28][29][30][31][32][33]). These graph width parameters are frequently explored in conjunction with obstruction, contributing to a robust body of research.…”

Section: Introductionmentioning

confidence: 99%

Filter for Submodular Partition Function: Connection to Loose Tangle

Fujita¹

2023

Preprint

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Loose Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). In this compact paper, we revisit and contemplate the interplay between Loose Tangle and Filter through the lens of a submodular partition function.

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Section: Introductionmentioning

confidence: 99%

Filter for Submodular Partition Function: Connection to Loose Tangle

Fujita¹

2023

Preprint

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“…Anchoring this issue is the work of Hicks and Brimkov [6], which revisits a classic paper authored by Hicks that appeared 16 years ago in Networks . These studies are rooted in concepts related to branch decomposition and branchwidth; these concepts can in turn be used to solve certain classes of combinatorial optimization problems.…”

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confidence: 99%

Preface

Raghavan

Smith

2020

Networks

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It has been a great pleasure for both of us to serve as Guest Co-Editors for this Special 50th Anniversary Issue of Networks. When the Editors-in-Chief invited us in early 2018 to guest edit this issue, we enthusiastically accepted. How could we not! Both of us have been associated with Networks for the past two decades. Raghu and Cole joined the editorial board in 1999 and 2005, respectively. Both of us published our first Networks paper in 2004, and both have been fortunate enough to be selected as winners of the annual Glover-Klingman prize for the best paper published annually in 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 10 papers appearing in this first of two special issues cover the history of Networks, update key developments that have been published in this field, and present new results that kick off ideas for the next half-century of networks research. The Editors-in-Chief of this journal since 1999, Drs. Bruce Golden and Doug Shier, begin the issue in [4] by discussing this journal's evolution over the past two decades. Frisch [3], who co-authored an article in Volume 1, Issue 1 of Networks, tells the story of the first three decades of Networks. (This article is a reprint of Frisch's 30-year history of Networks published in 2001.) Hochbaum [7] then presents new research on integer programming formulations that can be solved efficiently using combinatorial flow algorithms. The special class of problems considered in this paper are common across many classes of practical optimization problems, including those having network structures. The next set of articles are retrospective works on some of the most-studied application areas of network modeling and algorithms. Nagurney [8] examines network-based developments in economics and finance over the last half-century, with a particular eye toward the role of Networks in disseminating those contributions. This overview covers network optimization in network game theory, equilibrium models, and dynamical systems. Wang and Wasil [10] follow this article with a 50-year retrospective of vehicle routing problems, noting in particular that Networks has published over 140 articles in this area since its inception, and thus stands as one of the world's foremost sources for this important research field. Related to vehicle routing is the field of arc routing, reviewed in the work of Corberan et al. [2]. Their article serves as a tutorial for those seeking to understand arc routing models, as a survey of the literature in this field, and also as a prospective discussion of emerging ...

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Tangle bases: Revisited

Cited by 2 publications

References 67 publications

Filter for Submodular Partition Function: Connection to Loose Tangle

Filter for Submodular Partition Function: Connection to Loose Tangle

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