Dynamic Binary Search Trees: Improved Lower Bounds for the Greedy-Future Algorithm

Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be dynamic (i.e. change by rotations between searches), we still do not know how to compute the optimal algorithm (OPT) for a given sequence. One of the candidate algorithms whose serving cost is suspected to be optimal up-to a (multiplicative) constant factor is known by the name Greedy Future (GF). In an equivalent geometric way of representing queries on BSTs, GF is in fact equivalent to another algorithm called Geometric Greedy (GG). Most of the results on GF are obtained using the geometric model and the study of GG. Despite this intensive recent fruitful research, the best lower bound we have on the competitive ratio of GF is 4/3. Furthermore, it has been conjectured that the additive gap between the cost of GF and OPT is only linear in the number of queries. In this paper we prove a lower bound of 2 on the competitive ratio of GF, and we prove that the additive gap between the cost of GF and OPT can be ?(m ? log log n) where n is the number of items in the tree and m is the number of queries

Enchantment and the mechanical: an autoethnographic inquiry into leadership framed within a cosmic and ecological story

What difference would it make writing and sharing autoethnographic stories that locate self within the context of ecology and evolutionary cosmology? How might it change the way I understood my role as a leader of an environmental education charity? Would it help me to step into, let go of and share power? Through this inquiry I have recognised myself as being indigenous to the Cosmos; an identity which I maintain provides context and foundation for collaborative leadership. It is an identity that liberates inherited and often unconscious views of the universe as a machine of separate parts into a living story which endlessly reveals the dynamics of an integrated whole. As a fifth-generation, Pākehā, (New Zealander of European descent) working in a multicultural setting in the centre of London, I needed to understand two fundamental and seemingly opposing forces that motivate me. One is the opportunistic and single minded drive of the pioneer and the other is a pull to deeper values of connection and wholeness. What shaped my values? Excavating the past made me curious about the shadow colonialism has cast upon the present. I noticed my ambivalence towards the word ‘leadership’ despite being in leadership roles for many years. I paid attention to discomfort in the face of difference and discord. Recognising fractures within a culture built on Arcadian idealism held clues to limited notions of leadership that influenced my behaviour. The Three Baskets of Knowledge, drawn from Māori mythology, helped me find ground beneath the fault lines of the past. Listening to the land and looking back into the depths of time I drew meaning and direction from an ancient and emerging story. Within the 14-billion year account of our origins that science is now revealing, I came home to my own story. I identified with what I consider to be a contemporary form of indigeneity; cosmic indigeneity. I came to welcome non-idealised ways of being and the unpredictable nature of life itself. I learnt to embrace a process of leadership that is fluid and changing, sometimes singular and often collaborative

A declaration of caring: Towards ecological masculinism

This dissertation argues that the social and environmental problems we face are primarily the result of patriarchal or ‘malestream’ norms. These norms are constructed on hypermasculinist ways of being, thinking and doing that inhibit the growth and development of sustainable principles and practices. Responding to this assertion and following in the footsteps of deep ecology, social ecology and ecological feminism, the study brings masculinities concerns to the heart of the human/Nature relationship while also bringing concerns for society and the environment to the ways we think about men in the modern West. Further, it argues that if we are to achieve a truly sustainable future, then we must encourage men to reawaken their innate care. The dissertation declares that all men are born good and possess an infinite capacity to care and be caring. It is however recognised that these innate capacities for men to care and be caring are suppressed by ‘men’s oppression’ and that this oppression can prevent men from expressing their fullest humanness to the detriment of all Others and themselves. The dissertation recommends that men develop emotional competencies along with their intellect and intuition in order to authentically nurture the relational space between Others and themselves. Building on feminist care theory, a theoretical framework termed ecological masculinism is introduced, which facilitates modern Western men to care for and be caring towards society, Nature and the self—concurrently. The dissertation constructs a theoretical framework for ecological masculinism that is accompanied by a plurality of ecomasculine praxes. This ecologised masculinities theory and praxes instigates a new conversation in environmental philosophy that facilitates the rise of ‘ecomen’ who serve important roles in forging a deep green future for all of life on Earth

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum