IA Scholar Query: Packing Circuits in Eulerian Digraphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 29 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Lifted edges as connectivity priors for multicut and disjoint paths
https://scholar.archive.org/work/edizj43isvflhhihrsapdwjlhu
This work studies graph decompositions and their representation by 0/1 labeling of edges. We study two problems. The first is multicut (MC) which represents decompositions of undirected graphs (clustering of nodes into connected components). The second is disjoint paths (DP) in directed acyclic graphs where the clusters correspond to nodedisjoint paths. Unlike an alternative representation by node labeling, the number of clusters is not part of the input but is fully determined by the costs of edges. I would like to thank all my co-authors for a pleasant and constructive cooperation. Besides my supervisor Paul Swoboda, I would like to name especially Roberto Henschel, Timo Kaiser, Bjoern Andres, and Jan-Hendrik Lange for their major contribution to the shared publications that are part of this thesis. The publications could not be realized without their part of the work. I would like to thank Bjoern Andres for his supervision and help during the work on our common paper. I would like to mention also Michal Rolinek who helped us with our latest publication. I would like to thank Jiles Vreeken, Marcel Schulz and Markus List who cooperated with me on a research project that is not part of this thesis. I am very grateful to Bernt Schiele, the director of our department, who provided me with good working conditions, fully supported me in combining my working duties with family, and found a solution in the difficult stage of my PhD study by finding a new supervisor. Also, other people at MPI and Saarland University helped me to organize my work and family life and helped me with administrative issues.Andrea Hornakova, Universität Des Saarlandeswork_edizj43isvflhhihrsapdwjlhuMon, 29 Aug 2022 00:00:00 GMTSteiner Type Packing Problems in Digraphs: A Survey
https://scholar.archive.org/work/uc5dodxzgfe2fbo5wt7jnewz2u
In this survey we overview known results on several Steiner type packing problems in digraphs. The paper is divided into five sections: introduction, directed Steiner tree packing problem, strong subgraph packing problem, strong arc decomposition problem, directed Steiner cycle packing problem. This survey also contains some conjectures and open problems for further study.Yuefang Sunwork_uc5dodxzgfe2fbo5wt7jnewz2uSat, 20 Aug 2022 00:00:00 GMTPerfect Out-forests and Steiner Cycle Packing in Digraphs
https://scholar.archive.org/work/ayv7pvz6nvchxp3bo576iec6ua
In this paper, we study the complexity of two types of digraph packing problems: perfect out-forests problem and Steiner cycle packing problem. For the perfect out-forest problem, we prove that it is NP-hard to decide whether a given strong digraph contains a 1-perfect out-forest. However, when restricted to a semicomplete digraph D, the problem of deciding whether D contains an i-perfect out-forest becomes polynomial-time solvable, where i∈{0,1}. We also prove that it is NP-hard to find a 0-perfect out-forest of maximum size in a connected acyclic digraph, and it is NP-hard to find a 1-perfect out-forest of maximum size in a connected digraph. For the Steiner cycle packing problem, when both k≥ 2, ℓ≥ 1 are fixed integers, we show that the problem of deciding whether there are at least ℓ internally disjoint directed S-Steiner cycles in an Eulerian digraph D is NP-complete, where S⊆ V(D) and |S|=k. However, when we consider the class of symmetric digraphs, the problem becomes polynomial-time solvable. We also show that the problem of deciding whether there are at least ℓ arc-disjoint directed S-Steiner cycles in a given digraph D is NP-complete, where S⊆ V(D) and |S|=k.Yuefang Sunwork_ayv7pvz6nvchxp3bo576iec6uaThu, 18 Aug 2022 00:00:00 GMTCycle structure and colorings of directed graphs
https://scholar.archive.org/work/4oljppo7pnh3vlrxkkkho6zd4m
This thesis deals with problems from the theory of finite directed graphs. A directed graph (digraph for short) is a binary relation whose domain has finite size. With that digraphs can be seen as a very general way of representing (possibly asymmetric) relations between pairs from a finite set of objects. Undoubtedly, such a generality allows to encode many structures by digraphs. This works particularly well if important properties of the structure at hand can be expressed as relations or connections between objects. To give some selected examples, let us mention road networks, electricity networks, radio networks, the world wide web, circuits in electronic devices, or neural networks. A main focus of the thesis at hand is the investigation of properties of one of the most fundamental objects all over graph theory, the so-called cycle (sometimes also called circuit). A cycle in a graph is determined by a closed alternating sequence of cyclically connected vertices and edges. In a graph of finite size one will typically see loads of distinct cycles of various types. Therefore cycles constitute an important and recurring motive in almost all branches of graph theory, for instance, they play important roles in structural graph theory, in the theory of flows on directed networks, in theoretical characterizations of graph classes, as well as in the theory of graph colorings. Additionally, cycles play a decisive role in numerous algorithmic problems and their solutions, such as in the Traveling Salesman Problem, algorithms for finding a largest matching in a given graph, in the max-flow problem, and also in subprocedures such as Kruskal's algorithm for finding a minimum weight spanning tree. For those reasons, a substantial amount of research in graph theory has specialised on the structure of cycles in graphs. In the first major part of this thesis we deal with cycles which occur in directed graphs, and prove several necessary and sufficient theoretical conditions for the existence of cycles of certain types. Additi [...]Raphael Mario Steiner, Technische Universität Berlin, Stefan Felsnerwork_4oljppo7pnh3vlrxkkkho6zd4mThu, 30 Dec 2021 00:00:00 GMTPacking Strong Subgraph in Digraphs
https://scholar.archive.org/work/5sqfkuva45fzlg2wn6huhka73y
In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem. These problems can be viewed as generalizations of the famous Steiner tree packing problem and are closely related to the strong arc decomposition problem. We first prove the NP-completeness for the internally disjoint strong subgraph packing problem restricted to symmetric digraphs and Eulerian digraphs. Then we get inapproximability results for the arc-disjoint strong subgraph packing problem and the internally disjoint strong subgraph packing problem. Finally we study the arc-disjoint strong subgraph packing problem restricted to digraph compositions and obtain some algorithmic results by utilizing the structural properties.Yuefang Sun, Gregory Gutin, Xiaoyan Zhangwork_5sqfkuva45fzlg2wn6huhka73yMon, 25 Oct 2021 00:00:00 GMT