On the Complexity of Universal Leader Election

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This article focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most "obvious" complexity bounds have not been proven for randomized algorithms. In particular, the seemingly obvious lower bounds of Ω(m) messages, where m is the number of edges in the network, and Ω(D) time, where D is the network diameter, are nontrivial to show for randomized (Monte Carlo) algorithms. (Recent results, showing that even Ω(n), where n is the number of nodes in the network, is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms, except for the restricted case of comparison algorithms, where it was also required that nodes may not wake up spontaneously and that D and n were not known. We establish these fundamental lower bounds in this article for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (namely, algorithms that work for all graphs), apply to every D, m, and n, and hold even if D, m, and n are known, all the nodes wake up simultaneously, and the algorithms can make any use of node's identities. To show that these bounds are tight, we present an O(m) messages algorithm. An O(D) time leader election algorithm is known. A slight adaptation of our lower bound technique gives rise to an Ω(m) message lower bound for randomized broadcast algorithms. 

An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. The answer is known to be negative in the deterministic setting. We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that tradeoff messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.

Seeking the sun in deep, dark places: mesopelagic sightings of ocean sunfishes (Molidae)

Evidence is presented from publicly available remotely operated vehicle (ROV) footage that suggests deep-water ranging in ocean sunfishes (family Molidae) is more common than typically thought, including a new maximum depth recorded for the southern sunfish Mola ramsayi.

Effective collision strengths for election impact excitation of Cl III

Effective collision strengths for electron-impact excitation of the phosphorus-like ion Cl III are presented for all fine-structure transitions among the levels arising from the lowest 23 LS states. The collisional cross sections are computed in the multichannel close-coupling R-matrix approximation, where sophisticated configuration-interaction wave functions are used to represent the target states. The 23 LS states are formed from the basis configurations 3s²3p³, 3s3p⁴, 3s²3p²3d, and 3s²3p²4s, and correspond to 49 fine-structure levels, leading to a total possible 1176 fine-structure transitions. The effective collision strengths, obtained by averaging the electron collision strengths over a Maxwellian distribution of electron velocities, are tabulated in this paper for all 1176 transitions and for electron temperatures in the ranges T(K)=7500-25,000 and log T(K)=4.4-5.4. The former range encompasses the temperatures of particular importance for application to gaseous nebulae, while the latter range is more applicable to the study of solar and laboratory-type plasmas. © 2001 Academic Press.

Bringing down the walls: Is the notion of ‘promoting shared space’ commensurate with effective transformation of contested places in Belfast?

This article is a reflexive and critical examination of recent empirical research on effective practice in the management and ‘transformation’ of contested urban space at sectarian interfaces in Belfast. By considering the development of interfaces, the areas around them and policy responses to their persistence, the reality of contested space in the context of ‘peace building’ is apparent; with implications for local government as central to the statutory response. Belfast has developed an inbuilt absence of connectivity; where freedom of movement is particularly restricted and separation of contested space is the policy default position. Empirical research findings focus attention on the significance of social and economic regeneration and fall into three specific areas that reflect both long-term concerns within neighbourhoods and the need for adequate policy responses and action ‘on the ground’. Drawing on Elden and Sassen we reconfigure the analytical framework by which interfaces are defined, with implications for policy and practice in post-conflict Belfast. Past and current policy for peace-building in Northern Ireland, and transforming the most contested space, at interfaces in Belfast, is deliberately ambiguous and offers little substance having failed to advance from funding-led linguistic compliance to a sustainable peace-building methodology.