| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We have shown that for an undirected graph with n vertices and m edges, Depth-First Search (DFS) is possible using n+o(n) bits of memory. For a directed acyclic graph, DFS is possible using n/[exp(Omega(root(log n))) ] bits of memory. We have also obtained similar results for several other graph problems. Recently, researchers are finding more and more interesting connections between Exponential-Time Hypothesis (ETH) and the time complexity of polynomial-time solvable problems. For example, it is now known that ETH implies that a truly sub-cubic algorithm does *not* exist for a certain graph problem. Our results above seem to suggest that we should investigate space-complexity analogues of this phenomena: What are the consequences of the conjecture "Problem A requires linear space" ?
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