In this paper, we address the scheduling problem in wireless ad hoc networks by exploiting the computational advantage that comes when such scheduling problems can be represented by clawfree conflict graphs where we consider a wireless broadcast medium. It is possible to formulate a scheduling problem of network coded flows as finding maximum weighted independent set (MWIS) in the conflict graph of the network. Finding MWIS of a general graph is NP-hard leading to an NPhard complexity of scheduling. In a claw-free conflict graph, MWIS can be found in polynomial time leading to a throughput-optimal scheduling. We show that the conflict graph of certain wireless ad hoc networks are claw-free. In order to obtain claw-free conflict graphs in general networks, we suggest introducing additional conflicts (edges) while keeping the decrease in MWIS size minimal. To this end, we introduce an iterative optimization problem to decide where to introduce edges and investigate its efficient implementation. Besides, we exemplify some physical modifications to manipulate the conflict graph of a network and also propose a mixed scheduling strategy for specific networks. We conclude that claw breaking method by adding extra edges can perform nearly optimal under the necessary assumptions.
We consider decentralized stochastic multi-armed bandit problem with multiple players in the case of different communication probabilities between players. Each player makes a decision of pulling an arm without cooperation while aiming to maximize his or her reward but informs his or her neighbors in the end of every turn about the arm he or she pulled and the reward he or she got. Neighbors of players are determined according to an Erdős-Rényi graph with connectivity α which is reproduced in the beginning of every turn. We consider i.i.d. rewards generated by a Bernoulli distribution and assume that players are unaware about the arms' probability distributions and their mean values. In case of a collision, we assume that only one of the players who is randomly chosen gets the reward where the others get zero reward. We study the effects of α, the degree of communication between players, on the cumulative regret using well-known algorithms UCB1, -Greedy and Thompson Sampling.
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