Topic
Multigraph
About: Multigraph is a research topic. Over the lifetime, 1631 publications have been published within this topic receiving 26189 citations. The topic is also known as: pseudograph.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: A graph theoretic formulation for the train timetabling problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant is proposed, used to derive an integer linear programming model that is relaxed in a Lagrangian way.
Abstract: The train timetabling problem aims at determining a periodic timetable for a set of trains that does not violate track capacities and satisfies some operational constraints. In particular, we concentrate on the problem of a single, one-way track linking two major stations, with a number of intermediate stations in between. Each train connects two given stations along the track (possibly different from the two major stations) and may have to stop for a minimum time in some of the intermediate stations. Trains can overtake each other only in correspondence of an intermediate station, and a minimum time interval between two consecutive departures and arrivals of trains in each station is specified.In this paper, we propose a graph theoretic formulation for the problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant. This formulation is used to derive an integer linear programming model that is relaxed in a Lagrangian way. A novel feature of our model is that the variables in the relaxed constraints are associated only with nodes (as opposed to arcs) of the aforementioned graph. This allows a considerable speed-up in the solution of the relaxation. The relaxation is embedded within a heuristic algorithm which makes extensive use of the dual information associated with the Lagrangian multipliers. We report extensive computational results on real-world instances provided from Ferrovie dello Stato SpA, the Italian railway company, and from Ansaldo Segnalamento Ferroviario SpA.
579 citations
TL;DR: A simple, linear-time algorithm for the graph l-partition problem is presented and it is shown that if p−r≥n−1/2+ϵ for some constant ϵ, then the algorithm finds the optimal partition with probability 1− exp(−nΘ(e)).
Abstract: The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups. We present a simple, linear-time algorithm for the graph l-partition problem and we analyze it on a random “planted l-partition” model. In this model, the n nodes of a graph are partitioned into l groups, each of size n/l; two nodes in the same group are connected by an edge with some probability p, and two nodes in different groups are connected by an edge with some probability r
484 citations
1 Jan 1989
TL;DR: In this paper, a generalization of the definition of zeta function is presented, and the computation of Zx(u) for some well known families of graphs is discussed.
Abstract: Publisher Summary This chapter focuses on zeta functions of finite graphs and representations of p-adic groups. It discusses two different subjects: first is a combinatorial problem in algebraic graph theory, and the other is arithmetic of discrete subgroups of p-adic groups and their representations. The chapter presents the notation and basic definitions in graph theory. It also presents a generalization of the definition of zeta function. Spectrum of a finite multigraph is analyzed in the chapter. Moreover, the chapter also describes harmonic functions and the Hodge decomposition. The chapter also presents the computation of zeta functions Zx(u) for some well known families of graphs. These computations give many examples of graphs that are not Ramanujan graphs.
429 citations
TL;DR: The algebraic definitions presented here are motivated by the search for an adequate formalization of the concepts of social roles as regularities in social network patterns and represent significant homomorphic reductions of social networks which are possible using these defimtions to capture the role structure of a network.
401 citations
TL;DR: This paper generalizes Janssen′s result on complete bipartite graphs Km, n with m ≠ n and answers a question of Dinitz about the list chromatic index.
369 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 19 |
| 2024 | 36 |
| 2023 | 71 |
| 2022 | 101 |
| 2021 | 63 |
| 2020 | 76 |