Results 1 
8 of
8
Efficient Algorithms for Online Decision Problems
 J. Comput. Syst. Sci
, 2003
"... In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants [13, 18, 4] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when t ..."
Abstract

Cited by 138 (3 self)
 Add to MetaCart
In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants [13, 18, 4] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithms is inefficient for such large problems. For some problems with nice structure, specialized efficient solutions have been developed [10, 16, 17, 6, 3].
The Online Set Cover Problem
 STOC'03
, 2003
"... Let X = {1, 2,...,n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives eleme ..."
Abstract

Cited by 43 (5 self)
 Add to MetaCart
Let X = {1, 2,...,n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives elements to the algorithm from X onebyone. Once a new element is given, the algorithm has to cover it by some set of S containing it. We assume that the elements of X and the members of S are known in advance to the algorithm, however, the set X ′ ⊆ X of elements given by the adversary is not known in advance to the algorithm. (In general, X ′ may be a strict subset of X.) The objective is to minimize the total cost of the sets chosen by the algorithm. Let C denote the family of sets in S that the algorithm chooses. At the end of the game the adversary also produces (offline) a family of sets COPT that covers X ′. The performance of the algorithm is the ratio
Splay trees, DavenportSchinzel sequences, and the deque conjecture
, 2007
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations require O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.
unknown title
"... Abstract Let X = f1; 2; : : : ; ng be a ground set of n elements, and let S be a family of subsets of X, jSj = m, with a positive cost cS associated with each S 2 S. ..."
Abstract
 Add to MetaCart
Abstract Let X = f1; 2; : : : ; ng be a ground set of n elements, and let S be a family of subsets of X, jSj = m, with a positive cost cS associated with each S 2 S.
The Online Set Cover Problem (Extended Abstract)
"... Let X = {1, 2,..., n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈ S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives ele ..."
Abstract
 Add to MetaCart
Let X = {1, 2,..., n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈ S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives elements to the algorithm from X onebyone. Once a new element is given, the algorithm has to cover it by some set of S containing it. We assume that the elements of X and the members of S are known in advance to the algorithm, however, the set X ′ ⊆ X of elements given by the adversary is not known in advance to the algorithm. (In general, X ′ may be a strict subset of X.) The objective is to minimize the total cost of the sets chosen by the algorithm. Let C denote the family of sets in S that the algorithm chooses. At the end of the game the adversary also produces (offline) a family of sets COP T that covers X ′. The performance of the algorithm is the ratio between the cost of C and the cost of COP T. The maximum ratio, taken over all input sequences, is the competitive ratio of the algorithm. We present an O(log m � log n) competitive � deterministic algorithm for the problem, and estab
and the Deque Conjecture
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct ..."
Abstract
 Add to MetaCart
We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations take only O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures. 1
Follow the Leader for Online Optimization
, 2002
"... Linear optimization is a central algorithmic problem with many applications. In this paper, we consider a natural online version: the optimization problem has to be solved repeatedly over a sequence of periods, where the objective direction for the upcoming period is unknown. This models online vers ..."
Abstract
 Add to MetaCart
Linear optimization is a central algorithmic problem with many applications. In this paper, we consider a natural online version: the optimization problem has to be solved repeatedly over a sequence of periods, where the objective direction for the upcoming period is unknown. This models online versions of wellknown optimization problems, such as maxcut, variants of clustering, and also the classic online binary search tree problem. We present algorithms for these problem which are (1 + o(1))competitive with the optimal static solution chosen in hindsight. Our algorithms and proofs are motivated by geometric considerations.
The Online Set Cover Problem
"... Let X = {1, 2,..., n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈ S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives ele ..."
Abstract
 Add to MetaCart
Let X = {1, 2,..., n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈ S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives elements to the algorithm from X onebyone. Once a new element is given, the algorithm has to cover it by some set of S containing it. We assume that the elements of X and the members of S are known in advance to the algorithm, however, the set X ′ ⊆ X of elements given by the adversary is not known in advance to the algorithm. (In general, X ′ may be a strict subset of X.) The objective is to minimize the total cost of the sets chosen by the algorithm. Let C denote the family of sets in S that the algorithm chooses. At the end of the game the adversary also produces (offline) a family of sets COP T that covers X ′. The performance of the algorithm is the ratio