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This paper addresses the problem of generating conflict-free train schedules on a microscopic model of the railway infrastructure. Conflicts arise if two or more trains are scheduled to block the same track section at the same time. A standard model for this problem is the so-called conflict graph, where each considered train path corresponds to a vertex, and edges represent pairwise conflicts so that a conflict-free schedule corresponds to a maximum independent set. Because the linear programming relaxation of the conflict graph formulation is typically very weak, we develop an alternative model using the sequence of resources that each train path passes, encoded in a resource tree. For each resource, we can efficiently determine the maximal conflict cliques by scanning through the blocking times of all train paths and use these cliques as strong cutting planes in an integer linear programming formulation. We show that the number of maximal conflict cliques is linear in the number of train paths, so the ILP formulation uses much fewer but stronger constraints compared to the conflict graph model. In tests with real-world data from the Swiss Federal Railways, the new Resource Tree Conflict Graph model generates for major stations within seconds, even though the underlying model contains about half a million binary variables. This corresponds to a reduction of the computation time of roughly two orders of magnitude when compared to previous approaches and thus allows us to tackle considerable larger problem instances.

The importance of school leadership and workplace stress is a recurring theme in education-based research. The literature reports that workplace stress in teaching is a difficult matter to resolve, with mixed outcomes from interventions. The aim of this initial scoping study was to report on the experiences of school leaders with interpersonal conflict (IPC), a known cause of this workplace stress. Accordingly, a sample of twelve school leaders working in Irish post primary schools were recruited to participate in this study using semi-structured interviews. All twelve participants reported experiencing workplace stress and linked other people as a source of this stress. Nine out of twelve had experienced IPC as a school leader. School leaders also noted a fear of reporting workplace stress. Half of the participants reported becoming ill from workplace stress and had taken time off from work. Participants also reported ‘balkanisation’ of like-minded cliques that tried to exert control over other groups. None of the participants expressed confidence in organisational strategies to resolve workplace stress or IPC. This study demonstrates that resolutions for IPC were scant. Further research is needed to conceptualise this phenomenon in the school environment and to support school leaders to effectively manage IPC as a cause of workplace stress.

We model a community of individuals whose relationships are governed by the rules of the so-called Heider balance theory, but modified to address the impact of tolerating intolerant individuals. To consider tolerance toward a different group, the elements are assigned one of the two flags, A or B, and the elements of each group can be tolerant or intolerant. Two additional parameters, p and q, respectively, characterize the propensity of elements to cooperate and the propensity of tolerants to reject intolerant attitudes. We find that (1) parameter q does not affect the degree of conflict at the micro level, but has an important influence on the degree of conflict in the whole system; (2) segregation into two cliques occurs whenever there exists intolerants in both groups; (3) when intolerants are present in only one of the groups, segregation can be avoided for appropriate combinations of parameters p and q that depend on the fraction of intolerants and the size of the groups; (4) as the size of the system increases, two balanced solutions dominate: segregation into two cliques or the isolation of intolerants; and (5) endemic partially balanced configurations are observed in large systems.

The International Timetabling Competition 2019 (ITC 2019) posed a university timetabling problem involving assigning classes to times and rooms for an entire semester while assigning students to required classes. We propose a new mixed integer programming (MIP) formulation of the problem. The MIP formulation takes advantage of different graph structures in conflict graphs to construct a strong formulation of the constraints. In addition, we introduce a reduction algorithm that removes redundancies from the input data. We show that the reduction algorithm, combined with the graph-based MIP formulation, outperforms the MIP formulated by Holm et al. (A MIP formulation of the International Timetabling Competition 2019 problem, 2020) and thus becomes the new state-of-the-art MIP formulation for the ITC 2019. This paper reports the graph-based MIP formulation, which we used during the ITC 2019, and discusses additional approaches that one can use to strengthen the MIP.

Mantel Theorem and Turán Theorem are fundamental results in extremal graph theory. In this note, we present short proofs of these two theorems. Our proof shows that we essentially can reduce the proof of Turán Theorem to the minimum degree condition for cliques.

Purpose Studies of gang violence typically use police reports to investigate the structure of gang conflict, but overreliance on a singular data source could impede crime control efforts. Extending networked criminology, this study aims to explore what court records reveal about the directionality of gang conflicts. Design/methodology/approach Controlling for the presence of a civil gang injunction (CGI), the authors use multivariate quadratic assignment procedure regression models to disentangle factors thought to account for structural patterns of gang violence mapped from 933 prosecutions involving 307 gangs associated with violent conflict affecting the City of Los Angeles (1998–2013). Specifically, the authors compare competitive advantage to the explanatory power of turf proximity. Findings One measure of turf proximity outperforms all other explanatory factors – gangs with turf centrally positioned in a turf adjacency matrix are significantly more likely to launch attacks, be victimized and exhibit the highest levels of imbalance in their violent involvements. Regarding competitive advantage, the number of cliques and level of internal conflict are significant. Finally, being subject to a CGI is associated with initiating violence. Originality/value Court cases offer a feasible alternative to police data when investigating patterns of intergroup street gang violence.

The 0–1-knapsack problem is a well-known NP-hard problem in combinatorial optimization. We consider the extensions to the knapsack problem with conflict graph (KCG) and the knapsack problem with forcing graph (KFG). KCG has first been introduced by Yamada et al. and represents incompatibilities between items of the knapsack instance. KFG has been introduced by Pferschy and Schauer and represents the necessity of items for other items. Within this paper we provide pseudo-polynomial solutions for KCG and KFG with co-graphs as conflict and forcing graphs and extend these solutions to conflict and forcing graphs of bounded clique-width. Our solutions are based on dynamic programming using the tree-structure representing the conflict graph and the forcing graph. Further we conclude fully polynomial time approximation schemes for KCG on conflict graphs of bounded clique-width and KFG on forcing graphs of bounded clique-width. This generalizes the known results for conflict graphs and forcing graphs of bounded tree-width of Pferschy and Schauer.

Offers a developmental explanation for girlfighting and pathways to build girl allies For some time, reality TV, talk shows, soap-operas, and sitcoms have turned their spotlights on women and girls who thrive on competition and nastiness. Few fairytales lack the evil stepmother, wicked witch, or jealous sister. Even cartoons feature mean and sassy girls who only become sweet and innocent when adults appear. And recently, popular books and magazines have turned their gaze away from ways of positively influencing girls' independence and self-esteem and towards the topic of girls' meanness to other girls. What does this say about the way our culture views girlhood? How much do these portrayals affect the way girls view themselves? In Girlfighting , psychologist and educator Lyn Mikel Brown scrutinizes the way our culture nurtures and reinforces this sort of meanness in girls. She argues that the old adage \"girls will be girls\"-gossipy, competitive, cliquish, backstabbing- and the idea that fighting is part of a developmental stage or a rite-of-passage, are not acceptable explanations. Instead, she asserts, girls are discouraged from expressing strong feelings and are pressured to fulfill unrealistic expectations, to be popular, and struggle to find their way in a society that still reinforces gender stereotypes and places greater value on boys. Under such pressure, in their frustration and anger, girls (often unconsciously) find it less risky to take out their fears and anxieties on other girls instead of challenging the ways boys treat them, the way the media represents them, or the way the culture at large supports sexist practices. Girlfighting traces the changes in girls' thoughts, actions and feelings from childhood into young adulthood, providing the developmental understanding and theoretical explanation often lacking in other conversations. Through interviews with over 400 girls of diverse racial, economic, and geographic backgrounds, Brown chronicles the labyrinthine journey girls take from direct and outspoken children who like and trust other girls, to distrusting and competitive young women. She argues that this familiar pathway can and should be interrupted and provides ways to move beyond girlfighting to build girl allies and to support coalitions among girls. By allowing the voices of girls to be heard, Brown demonstrates the complex and often contradictory realities girls face, helping us to better understand and critique the socializing forces in their lives and challenging us to rethink the messages we send them.

The Silk Letters Conspiracy, or Case, was a plot by a small clique of Indian Pan-Islamists located in Afghanistan, India and the Hijaz to overthrow British rule in India during the First World War. Although British officials at the time were prepared to admit that the conspiracy had been 'organised with some skill', there was a general feeling that it was a rather 'pathetic' and 'ineffectual' affair, and 'crazy in the extreme'. This verdict has been echoed by those who have subsequently considered the plot, if only in passing. But there is more to the Silk Letters Conspiracy than meets the eye, as this article will detail. In retrospect, the Case has a greater significance than previously thought in terms of Britain's encounter with Pan-Islam.

Computational Approaches to Studying the Co-evolution of Networks and Behaviour in Social Dilemmas shows students, researchers, and professionals how to use computation methods, rather than mathematical analysis, to answer research questions for an easier, more productive method of testing their models. Illustrations of general methodology are provided and explore how computer simulation is used to bridge the gap between formal theoretical models and empirical applications.