By Udo Adamy, Thomas Erlebach (auth.), Roberto Solis-Oba, Klaus Jansen (eds.)
The Workshop on Approximation and on-line Algorithms (WAOA 2003) inquisitive about the layout and research of algorithms for on-line and computationally difficult difficulties. either different types of difficulties have loads of purposes ar- ing from various ?elds. The workshop additionally coated experimental study on approximation and on-line algorithms. WAOA 2003 came about in Budapest, Hungary, from September sixteen to September 18. The workshop was once a part of the ALGO 2003 occasion, which additionally hosted ESA 2003, WABI 2003, and ATMOS 2003. TopicsofinterestforWAOA2003were:competitiveanalysis,inapproximab- ityresults,randomizationtechniques,approximationclasses,scheduling,coloring and partitioning, cuts and connectivity, packing and overlaying, geometric pr- lems, community layout, and functions to video game conception and ?nancial difficulties. in line with our demand papers we obtained forty-one submissions. each one submission was once reviewed via a minimum of three referees, who judged the papers on originality, caliber, and consistency with the subjects of the convention. in line with those studies this system committee chosen 19 papers for presentation on the workshop and for e-book during this complaints. This quantity includes the nineteen chosen papers and five invited abstracts from an ARACNE minisymposium which happened as a part of WAOA.
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Additional info for Approximation and Online Algorithms: First International Workshop, WAOA 2003, Budapest, Hungary, September 16-18, 2003. Revised Papers
F ∈ F ) as well as facility f i (resp. fi ), for i ∈ [ n2 ]. , a speciﬁc actual input is chosen with probability equal to n1 . Since every potential input contains (exactly) one pair of complementary facilities, OP T can cover all n cities by opening the two complementary facilities, hence E[OP T ] = n + 2(2 − ). Denote by Af the cost of facilities opened by A. Note that 36 Spyros Angelopoulos E[Af ] = Pr(z ∈ I) · E[Af |z ∈ I] + Pr(z ∈ I) · E[Af |z ∈ I] 1 = (E[Af |z ∈ I] + E[Af |z ∈ I]). 2 (3) In order to show the wanted, we give expressions for E[Af |z ∈ I] and E[Af |z ∈ I]; the intuition is that not both expressions can be very small, hence E[Af ] is large.
No two jobs of diﬀerent size were scheduled on the same machine, and l2 > m 2 m or l3 > m or l2 < m 2 , or, equivalently, l3 < 2 2 . On the event the actual input is S, this implies that either two jobs in S of diﬀerent sizes are eventually scheduled on the same machine, or one of the following holds: A machine will be assigned at least 4 jobs of size 2, or a machine will be assigned at least 3 jobs of size 3 (depending on whether l3 > m , or l2 > m 2 2 , respectively). In each case, the makespan of A is at least 7.
We refer to the above representation of inputs as the facility-input model. A diﬀerent way of representing the input is to view the cities as the input items. Namely, the input consists of the set of all cities, with each city being identiﬁed by its id, and its distance to each facility. The opening costs of the facilities are treated as global information. In this context, an irrevocable decision is interpreted as assigning each considered city to some open facility, possibly opening a new facility, but without aﬀecting the assignment of cities considered in the past.
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