this algorithm, the bins are partitioned into $d$ groups of size $n/d$ and each ball picks one random bin from each group. The ball is then allocated to a least-loaded bin among the chosen bins, with ties broken in favor of the bin from the least-indexed group. The algorithm uses exponentially smaller number of choices and achieve a maximum load of $\frac{\log\log n}{d \phi_d } +{\mathcal{O}}(1)$, where $1{\leqslant}\phi_d{\leqslant}2$ is an specified constant. Byers et al. [@BCM04] studied a model, where $n$ bins are uniformly at random placed on a geometric space. Then each ball, in turn, picks $d$ locations in the space. Corresponding to these $d$ locations, the ball probes the load of $d$ bins that have the minimum distance from the locations. The ball then allocates itself to one of the $d$ bins with minimum load. In this scenario, the probability that a location close to a bin is chosen depends on the distribution of other bins in the space and hence there is not a uniform distribution over the potential choices. Here, the authors showed the maximum load is ${\log_d\log n}+{\mathcal{O}}(1)$. Later on, Kenthapadi and Panigrahy [@KP06] proposed a graphical balanced allocation in which bins are interconnected as a ${s}$-regular graph and each ball picks a random edge of the graph. It is then placed in one of its endpoints with a smaller load. This allocation algorithm results in a maximum load of $\log\log n+{\mathcal{O}}\left(\frac{\log n}{\log ({s}/\log^4 n)}\right)+{\mathcal{O}}(1)$. Godfrey [@God08] studied balanced allocation on hypergraphs where each ball probes the bins contained in a random edge of size $\Omega(\log n)$. [In [@BBFN12; @God08], the balanced allocation process on hypergraphs was studied where number of choices is $d = \Omega(\log n)$. The analysis involves the second moment method (Chernoff bounds), and lower bound on $d$ is needed in order to achieve concentration. Hence it is unlikely that the techniques of \[3,12\] can be extended to the range $d = o(\log n)$.]{} Peres et al. [@PT