331 research outputs found
On Covering a Graph Optimally with Induced Subgraphs
We consider the problem of covering a graph with a given number of induced
subgraphs so that the maximum number of vertices in each subgraph is minimized.
We prove NP-completeness of the problem, prove lower bounds, and give
approximation algorithms for certain graph classes.Comment: 9 page
Cache-Oblivious Selection in Sorted X+Y Matrices
Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A
by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for
selecting the k-th smallest element from A. We show how to make this algorithm
IO-efficient. Our cache-oblivious algorithm performs O((m+n)/B) IOs, where B is
the block size of memory transfers
Pants Decomposition of the Punctured Plane
A pants decomposition of an orientable surface S is a collection of simple
cycles that partition S into pants, i.e., surfaces of genus zero with three
boundary cycles. Given a set P of n points in the plane, we consider the
problem of computing a pants decomposition of the surface S which is the plane
minus P, of minimum total length. We give a polynomial-time approximation
scheme using Mitchell's guillotine rectilinear subdivisions. We give a
quartic-time algorithm to compute the shortest pants decomposition of S when
the cycles are restricted to be axis-aligned boxes, and a quadratic-time
algorithm when all the points lie on a line; both exact algorithms use dynamic
programming with Yao's speedup.Comment: 5 pages, 1 grayscale figur
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