Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of space-efficient polynomial-time algorithms for directed st- connectivity (STCON). Given a directed graph G, and a pair of vertices s, t, the STCON problem is to decide if there exists a path from s to t in G. For general graphs, the best polynomial-time algorithm for STCON uses space that is only slightly sublinear. Hover, for special classes of directed graphs, polynomial-time poly-logarithmic-space algorithms are known for STCON. ,  con- tinue this thread of researchand study a class of graphs called unique-path graphs with respect to source s, where there is at most one simple path from s to any vertex in the graph. For these graphs,  give a polynomial-time algorithm that uses ˜ O(n # ) space for any constant # ∈ (0,1).  also give a polynomial-time, ˜ O(n # )-space algorithm to recognize unique-path graphs. Unique-path graphs are related to configuration graphs of unambiguous log-space computations, but they can have some directed cycles. Our results may be vied along the continuum of sublinear-space polynomial- time algorithms for STCON in different classes of directed graphs - from slightly sublinear-space algorithms for general graphs to O(log n) space algorithms for trees.
['Sampath Kannan', 'Sanjeev Khanna', 'Sudeepa Roy']
I am writing a research paper on a idea STCON in Directed Unique-Path Graphs
[{"from": "human", "value": "I am writing a research paper on a idea STCON in Directed Unique-Path Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of space-efficient polynomial-time algorithms for directed st- connectivity (STCON). Given a directed graph G, and a pair of vertices s, t, the STCON problem is to decide if there exists a path from s to t in G. For general graphs, the best polynomial-time algorithm for STCON uses space that is only slightly sublinear. Hover, for special classes of directed graphs, polynomial-time poly-logarithmic-space algorithms are known for STCON. ,  con- tinue this thread of researchand study a class of graphs called unique-path graphs with respect to source s, where there is at most one simple path from s to any vertex in the graph. For these graphs,  give a polynomial-time algorithm that uses \u02dc O(n # ) space for any constant # \u2208 (0,1).  also give a polynomial-time, \u02dc O(n # )-space algorithm to recognize unique-path graphs. Unique-path graphs are related to configuration graphs of unambiguous log-space computations, but they can have some directed cycles. Our results may be vied along the continuum of sublinear-space polynomial- time algorithms for STCON in different classes of directed graphs - from slightly sublinear-space algorithms for general graphs to O(log n) space algorithms for trees."}]