Strip packing with precedence constraints and strip packing with release times
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Resource allocation in bounded degree trees
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Scheduling with conflicts: online and offline algorithms
Journal of Scheduling
Strip packing with precedence constraints and strip packing with release times
Theoretical Computer Science
Optimizing active ranges for consistent dynamic map labeling
Computational Geometry: Theory and Applications
First-Fit coloring of bounded tolerance graphs
Discrete Applied Mathematics
Max-coloring and online coloring with bandwidths on interval graphs
ACM Transactions on Algorithms (TALG)
A better approximation ratio and an IP formulation for a sensor cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
A constant factor approximation algorithm for the storage allocation problem: extended abstract
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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Dynamic storage allocation is the problem of packing given axis-aligned rectangles into a horizontal strip of minimum height by sliding the rectangles vertically but not horizontally. Where L= is the maximum sum of heights of rectangles that intersect any vertical line and OPT is the minimum height of the enclosing strip, it is obvious that $\ensuremath{\text{\it OPT}}\ge \ensuremath{\text{\it LOAD}}$; previous work showed that $\ensuremath{\text{\it OPT}}\le 3\cdot LOAD. We continue the study of the relationship between OPT and LOAD, proving that OPT=L+O((hmax/L)1/7)L, where hmax is the maximum job height. Conversely, we prove that for any $\epsilon0$, there exists a c0 such that for all sufficiently large integers $h_{\max}$, there is a dynamic storage allocation instance with maximum job height $h_{\max}$, maximum load at most L, and $\ensuremath{\text{\it OPT}}\geq L+c(h_{\max}/L)^{1/2+\epsilon}L$, for infinitely many integers L. En route, we construct several new polynomial-time approximation algorithms for dynamic storage allocation, including a $(2+\epsilon)$-approximation algorithm for the general case and polynomial-time approximation schemes for several natural special cases.