My research

"A new polynomial time heuristic for hamiltonian cycle problem using atomic cycle merging"

The algorithm first discovers all atomic cycles in a graph, then preprocesses the graph using this data to build an intermediate representation called cycle adjacency graph. This CAG maintains information to avoid local decisions leading to unreachability of a vertex and also to guide choice of merging cycles to obtain a larger cycles such that subsequently a hamiltonian cycle is obtained if it exists. This is similar to how a crystal forms, on a seed, the lattice expands.

"An Augmented breadth first search for the longest path problem"

The conventional Breadth First search classifies the edges of an undirected graph into tree edges and cross edges. The cross edges can be utilised to prune and implant branches to BFS tree at specific places to find longer paths from source to destination. Other operations such as rotation can also be performed to increase the height of the tree. This indirectly simulates the apical domination in real trees where the shoot tip inhibits growth of axillary buds to increase height of tree instead of breadth. The BFS search space doesnt include the dest. while building the BFS tree, but at the end it attaches dest. to all its neighbours as leaves...

"The art of designing search spaces"

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"A new heuristic for hamiltonian path problem using BFS directed DFS."

The problem with combinatorial problems is that the search space is highly non deterministic. For NPC problems, there is no inherent mathematical structure yet found, which can be exploited to build an exact polynomial time solution. The next choice then is to solve by search which if done via brute force is obviously exponenetial in time. Therefore, we try to perform the search intelligently such that we avoid exploring unfruitful parts of search space and devise some guiding mechanism to draw the search toward choices leading to a path to glabal optimal. While taking local decisions, its important to have some kind of global perpective as well to predict the consequences of local choice...

"An augmented Dijkstra's Algorithm as heuristic for the travelling salesman problem."

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"Sorting by Diffusion"

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