No abstract

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colourings for k-uniform hypergraphs with maximum degree ∆ if k ≥ 28 and q > 357∆ 14 k−14 . We also obtain a polynomial-time almost uniform sampler if q > 931∆ 16 k−16/3 . These are the first approximate counting and sampling algorithms in the regime q ≪ ∆ (for large ∆ and k) without any additional assumptions. Our method is based on the recent work of Moitra (STOC, 2017). One important contribution of ours is to remove the dependency of k and ∆ in Moitra's approach.

Recently, as it can greatly increase the capacity of cellular networks through spatial diversity, cooperative communications has been obtaining more and more attention. As a widely used schema, user (user equipment, UE) cooperation presents its advantage. However, due to the users' selfish nature, UE may be unwilling to serve as a relay node if they cannot obtain a corresponding reward. On the contrary, to save energy for longer standby time, particularly when there is energy shortage, many source users would like to purchase the relay service from other idle UE. Therefore, reconciling the demand of both sides is a challenging problem to be resolved. In this paper, a realistic double-auction scenario is constructed between multiple source UE and multiple idle UE in a cellular network. We take the avaricious psychology of network entities into consideration by determining the ask and bid prices through a markup, which is the function of their residual energy. To solve this doubleauction-based optimal relay assignment problem, we transform it into maximum matching (MM) and maximum weighted matching (MWM) problems, respectively, and we solve them by corresponding algorithms. Experimental results show that the proposed algorithms dramatically maximize the system performance involving successful source-relay pairs, system throughput, and social welfare (SW), compared with other idealized truthful double-auction scheme that only consider the system throughput.Index Terms-Cooperative communications, double auction, optimal relay assignment, wireless cellular networks.

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colourings for k-uniform hypergraphs with maximum degree ∆ if k ≥ 28 and q > 357∆ 14 k−14 . We also obtain a polynomial-time almost uniform sampler if q > 931∆ 16 k−16/3 . These are the first approximate counting and sampling algorithms in the regime q ≪ ∆ (for large ∆ and k) without any additional assumptions. Our method is based on the recent work of Moitra (STOC, 2017). One important contribution of ours is to remove the dependency of k and ∆ in Moitra's approach.A preliminary version of this paper appeared in 50th Annual ACM SIGACT Symposium on the Theory of Computing (STOC), 2018, Los Angeles.1 Interestingly, to prove the existence of frozen colourings, we also need to appeal to the local lemma.

Traditional search algorithm based on keywords, is easy to appear polysemy and synonyms phenomenon, which affects the recall and precision of search. And it uses a centralized search algorithm. Once the servers have problems, the whole system will be out of service. As a new distributed computing, Cloud computing has a high computing and mass storage. In order to reduce server load and increase the efficiency of resource discovery, this paper puts forward the search algorithm based on semantic in the cloud environment, which realizes intelligent search through the Chord precise search and semantic fuzzy matching fusion, and enhances the recall rate. Simulation experiment shows that the algorithm achieves high recall-precision, which performs the efficiency search in small-scale stable network.