Exponential Growth
As problem size increases, the number of possible solutions or states grows
exponentially, leading to significant increases in computational requirements
and difficulty in solving the problem.
Brute-force Approach
Trying every possible solution becomes impractical for large problems due to
the exponential growth in potential solutions, resulting in excessive
computation times.
Memory Usage
Large datasets or complex problems can exceed memory limits, making it
difficult to manage and process all required information effectively.
State Space Explosion
As problems grow, the number of possible states can rapidly exceed memory
capacity, complicating the management and processing of these states.
Algorithm Efficiency
Problems that are easy to verify but hard to solve from scratch may require
approximation algorithms to find near-optimal solutions when exact methods are
too slow.
Intractable Problems
Some problems, like the Halting Problem, are unsolvable by any algorithm.
NP-hard problems are particularly challenging and often require complex or
approximate solutions.
Practical Constraints
Computers have limitations in speed and memory, and time and financial
constraints can further impact the ability to solve complex problems
effectively.