Abstract. Given two functions f and g mapping nodes to non-negative integers, we give a silent self-stabilizing algorithm that computes a minimal (f, g)-alliance in an asynchronous network with unique node IDs, assuming that every node p has a degree at least g(p) and satisfies f (p) ≥ g(p). Our algorithm is safely converging in the sense that starting from any configuration, it first converges to a (not necessarily minimal) (f, g)-alliance in at most four rounds, and then continues to converge to a minimal one in at most 5n+4 additional rounds, where n is the size of the network. Our algorithm is written in the shared memory model. It is proven assuming an unfair (distributed) daemon. Its memory requirement is O(log n) bits per process, and it takes O(∆ 3 n) steps to stabilize, where ∆ is the degree of the network.
In this paper, we address the deterministic rendezvous in graphs where k mobile agents, disseminated at different times and different nodes, have to meet in finite time at the same node. The mobile agents are autonomous, oblivious, labeled, and move asynchronously. Moreover, we consider an undirected anonymous connected graph. For this problem, we exhibit some asymptotical time and space lower bounds as well as some necessary conditions. We also propose an algorithm that is asymptotically optimal in both space and round complexities.
International audienceIn this paper, we address the deterministic rendezvous of mobile agents into any unoriented connected graph. The agents are autonomous, oblivious, move asynchronously. For this problem, we exhibit some time and space lower bounds as well as some necessary conditions. We also propose an algorithm that is space-optimal and asymptotically optimal in rounds
toxicity develops, other regimens such as multiagent chemotherapy or hysterectomy may be considered.In women with high-risk GTN, multiagent chemotherapy, along with surgery or radiation, is recommended. Survival rates exceed 86% for women with FIGO scores ≥ 7. Referral to a specialist is warranted for women with high-risk GTN, given the risk of metastasis particularly in the brain, liver and kidney.Once remission is achieved in women with GTN, serial hCG levels should be evaluated every 2 to 3 weeks in the first 3 months, then monthly for at least 12 months. The rate of recurrence after 1 year of remission among low-risk women is < 1%, but this rate is higher among high-risk women and may require additional monitoring every 6 to 12 months. During treatment and hCG monitoring, oral contraception is recommended. For future pregnancies, ultrasounds should be performed early due to the increased risk a second mole developing.In summary, GTD can be diagnosed and treated successfully in most women. The prompt and appropriate management of molar pregnancies can help to identify GTN and other related diseases early on.
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