  Updating and querying on a range is a classical algorithmic problem with a
multitude of applications. The Segment Tree data structure is particularly
notable in handling the range query and update operations. A Segment Tree
divides the range into disjoint segments and merges them together to perform
range queries and range updates elegantly. Although this data structure is
remarkably potent for 1-dimensional problems, it falls short in higher
dimensions. Lazy Propagation enables the operations to be computed in $O(logn)$
time in a single dimension. However, the concept of lazy propagation could not
be translated to higher-dimensional cases, which imposes a time complexity of
$O(n^{k-1} \; logn)$ for operations on $k$-dimensional data. In this work, we
have made an attempt to emulate the idea of lazy propagation differently so
that it can be applied for 2-dimensional cases. Moreover, the proposed
modification should be capable of performing most general aggregate functions
similar to the original Segment Tree, and can also be extended to even higher
dimensions. Our proposed algorithm manages to perform range sum queries and
updates in $O(\log^2 n)$ time for a 2-dimensional problem, which becomes
$O(\log^d n)$ for a $d$-dimensional situation.
