Deterministic fully dynamic graph algorithms are presented for connectivity, minimum spanning forest, a-edge connectivity, and biconnectivity. Assuming that we start with no edges in a graph with n vertices, the amortized operation cost0 arc O(log2 n) for connectivity and O(log4 n) for minimum spanning forest, 2+dgeconnectivity, and biconnectity.

We design top trees as a new simpler interface for data structures maintaining information in a fully dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of each tree in the forest. The forest can be updated by insertion and deletion of edges and by changes to vertex and edge weights. Each update is supported in O(log n) time, where n is the size of the tree(s) involved in the update. Also, we show how to support nearest common ancestor queries and level ancestor queries with respect to arbitrary roots in O(log n) time. Finally, with marked and unmarked vertices, we show how to compute distances to a nearest marked vertex. The latter has applications to approximate nearest marked vertex in general graphs, and thereby to static optimization problems over shortest path metrics.Technically speaking, top trees are easily implemented either with Frederickson's [1997a] topology trees or with Sleator and Tarjan's [1983] dynamic trees. However, we claim that the interface is simpler for many applications, and indeed our new bounds are quadratic improvements over previous bounds where they exist.This article includes work presented at ICALP'97 [Alstrup et al. 1997] and SWAT'00 [Alstrup et al. 2000].

Deterministic fully dynamic graph algorithms are presented for connectivity, minimum spanning tree, 2-edge connectivity, and biconnectivity. Assuming that we start with no edges in a graph with n vertices, the amortized operation costs are O (log 2 n ) for connectivity, O (log 4 n ) for minimum spanning forest, 2-edge connectivity, and O (log 5 n ) biconnectivity.

Climate change-related coral bleaching, i.e., the visible loss of zooxanthellae from the coral host, is increasing in frequency and extent and presents a major threat to coral reefs globally. Coral bleaching has been proposed to involve accelerating light stress of their microalgal endosymbionts via a positive feedback loop of photodamage, symbiont expulsion and excess in vivo light exposure. To test this hypothesis, we used light and O2 microsensors to characterize in vivo light exposure and photosynthesis of Symbiodinium during a thermal stress experiment. We created tissue areas with different densities of Symbiodinium cells in order to understand the optical properties and light microenvironment of corals during bleaching. Our results showed that in bleached Pocillopora damicornis corals, Symbiodinium light exposure was up to fivefold enhanced relative to healthy corals, and the relationship between symbiont loss and light enhancement was well-described by a power-law function. Cell-specific rates of Symbiodinium gross photosynthesis and light respiration were enhanced in bleached P. damicornis compared to healthy corals, while areal rates of net photosynthesis decreased. Symbiodinium light exposure in Favites sp. revealed the presence of low light microniches in bleached coral tissues, suggesting that light scattering in thick coral tissues can enable photoprotection of cryptic symbionts. Our study provides evidence for the acceleration of in vivo light exposure during coral bleaching but this optical feedback mechanism differs between coral hosts. Enhanced photosynthesis in relation to accelerating light exposure shows that coral microscale optics exerts a key role on coral photophysiology and the subsequent degree of radiative stress during coral bleaching.

No abstract