15 research outputs found
Scheduling unit-length jobs with machine eligibility restrictions
Department of Logistics2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
Tree Contractions and Evolutionary Trees
An evolutionary tree is a rooted tree where each internal vertex has at least
two children and where the leaves are labeled with distinct symbols
representing species. Evolutionary trees are useful for modeling the
evolutionary history of species. An agreement subtree of two evolutionary trees
is an evolutionary tree which is also a topological subtree of the two given
trees. We give an algorithm to determine the largest possible number of leaves
in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the
maximum degree d of these trees is bounded by a constant, the time complexity
is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this
algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d
sqrt(d) log^3(n)) time
On covering by translates of a set
In this paper we study the minimal number of translates of an arbitrary
subset of a group needed to cover the group, and related notions of the
efficiency of such coverings. We focus mainly on finite subsets in discrete
groups, reviewing the classical results in this area, and generalizing them to
a much broader context. For example, we show that while the worst-case
efficiency when has elements is of order , for fixed and
large, almost every -subset of any given -element group covers
with close to optimal efficiency.Comment: 41 pages; minor corrections; to appear in Random Structures and
Algorithm
IST Austria Technical Report
We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let denote the number of nodes of a graph, the number of edges (for constant treewidth graphs ) and the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of in time and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time , when the output is , as compared to the previously best known algorithm with running time . Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in time and the associated decision problem can be solved in time, improving the previous known and bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires time, improving the previous known bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks