On the termination of flooding

Flooding is among the simplest and most fundamental of all graph/network algorithms. Consider a (distributed network in the form of a) finite undirected graph G with a distinguished node v that begins flooding by sending copies of the same message to all its neighbours and the neighbours, in the next round, forward the message to all and only the neighbours they did not receive the message from in that round and so on. We assume that nodes do not keep a record of the flooding event, thus, raising the possibility that messages may circulate infinitely even on a finite graph. We call this history-less process amnesiac flooding (to distinguish from a classic distributed implementation of flooding that maintains a history of received messages to ensure a node never sends the same message again). Flooding will terminate when no node in G sends a message in a round, and, thus, subsequent rounds. As far as we know, the question of termination for amnesiac flooding has not been settled - rather, non-termination is implicitly assumed.In this paper, we show that surprisingly synchronous amnesiac flooding always terminates on any arbitrary finite graph and derive exact termination times which differ sharply in bipartite and non-bipartite graphs. In particular, synchronous flooding terminates in e rounds, where e is the eccentricity of the source node, if and only if G is bipartite, and, otherwise, in j rounds where e For comparison, we also show that, for asynchronous networks, however, an adaptive adversary can force the process to be non-terminating.</div

WRC Assessment re PCCS Garment Co. Ltd. (Cambodia): Findings, Recommendations and Status

WRC assessment detailing labor violations in the areas of health and safety, harassment and abuse, and legally-mandated benefits at a PCCS Garment factory in Cambodia

Worker Rights Consortium Assessment re Far East Garment Textile and First Apparel (Thailand): Findings, Recommendations, and Status Report

WRC reports on its assessment of labor violations at the Far East factory in Thailand. Includes a discussion of logistics of the assessment and recommendations for the company to remediate the problems

Rapid changes in ice core gas records Part 2: Understanding the rapid rise in atmospheric CO2 at the onset of the Bølling/Allerød

During the last glacial/interglacial transition the Earth's climate underwent rapid changes around 14.6 kyr ago. Temperature proxies from ice cores revealed the onset of the Bølling/Allerød (B/A) warm period in the north and the start of the Antarctic Cold Reversal in the south. Furthermore, the B/A is accompanied by a rapid sea level rise of about 20 m during meltwater pulse (MWP) 1A, whose exact timing is matter of current debate. In situ measured CO₂ in the EPICA Dome C (EDC) ice core also revealed a remarkable jump of 10&plusmn;1 ppmv in 230 yr at the same time. Allowing for the age distribution of CO₂ in firn we here show, that atmospheric CO₂ rose by 20–35 ppmv in less than 200 yr, which is a factor of 2–3.5 larger than the CO₂ signal recorded in situ in EDC. Based on the estimated airborne fraction of 0.17 of CO₂ we infer that 125 Pg of carbon need to be released to the atmosphere to produce such a peak. Most of the carbon might have been activated as consequence of continental shelf flooding during MWP-1A. This impact of rapid sea level rise on atmospheric CO₂ distinguishes the B/A from other Dansgaard/Oeschger events of the last 60 kyr, potentially defining the point of no return during the last deglaciation