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In this paper, we present a framework used to construct and analyze algorithms for online optimization problems with deadlines or with delay over a metric space. Using this framework, we present algorithms for several different problems. We present an $O(D^{2})$-competitive deterministic algorithm for online multilevel aggregation with delay on a tree of depth $D$, an exponential improvement over the $O(D^{4}2^{D})$-competitive algorithm of Bienkowski et al. (ESA 16), where the only previously-known improvement was for the special case of deadlines by Buchbinder et al. (SODA 17). We also present an $O(log^{2}n)$-competitive randomized algorithm for online service with delay over any general metric space of $n$ points, improving upon the $O(log^{4}n)$-competitive algorithm by Azar et al. (STOC 17). In addition, we present the problem of online facility location with deadlines. In this problem, requests arrive over time in a metric space, and need to be served until their deadlines by facilities that are opened momentarily for some cost. We also consider the problem of facility location with delay, in which the deadlines are replaced with arbitrary delay functions. For those problems, we present $O(log^{2}n)$-competitive algorithms, with $n$ the number of points in the metric space. The algorithmic framework we present includes techniques for the design of algorithms as well as techniques for their analysis.
We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not necessary. In parti
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The problems are r
We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner
Many discrete optimization problems amount to select a feasible subgraph of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is
In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some constraints. However,