Maxim Sviridenko

Learn More
A <i>separable assignment problem</i> (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, <i>f</i><inf><i>ij</i></inf>, for assigning item <i>j</i> to bin <i>i;</i> and a separate packing constraint for each bin - i.e. for bin <i>i</i>, a family <i>L</i><inf><i>i</i></inf> of subsets of items that fit in bin <i>i</i>. The goal(More)
We consider two types of buffering policies that are used in network switches supporting QoS (Quality of Service). In the <italic>FIFO</italic> type, packets must be released in the order they arrive; the difficulty in this case is the limited buffer space. In the <italic>bounded-delay</italic> type, each packet has a maximum delay time by which it must be(More)
We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with(More)
We consider the following problem: The Santa Claus has n presents that he wants to distribute among m kids. Each kid has an arbitrary value for each present. Let p<sub>ij</sub> be the value that kid i has for present j. The Santa's goal is to distribute presents in such a way that the least lucky kid is as happy as possible, i.e he tries to maximize(More)
A directed multigraph is said to be <i>d</i>-regular if the indegree and outdegree of every vertex is exactly <i>d</i>. By Hall's theorem, one can represent such a multigraph as a combination of at most <i>n</i><sup>2</sup> cycle covers, each taken with an appropriate multiplicity. We prove that if the <i>d</i>-regular multigraph does not contain more than(More)
In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic (\pipage") procedure of rounding of linear relaxations. By using the method we design a (1 ? (1 ? 1=k) k)-approximation algorithm for the(More)
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is(More)
We study the following packing problem: Given a collection of d-dimensional rectangles of specified sizes, pack them into the minimum number of unit cubes. We show that unlike the one-dimensional case, the two-dimensional packing problem cannot have an asymptotic polynomial time approximation scheme (APTAS), unless P = NP . On the positive side, we give an(More)