arXiv subjects

Piotr Sankowski

Publications and source records attributed to Piotr Sankowski.

60 records · Page 4Linked to original sources

arXiv2012

Structural and electronic properties of Pb1-xCdxTe and Pb1-xMnxTe ternary alloys

A systematic theoretical study of two PbTe-based ternary alloys, Pb1-xCdxTe and Pb1-xMnxTe, is reported. First, using ab initio methods we study the stability of the crystal structure of CdTe - PbTe solid solutions, to predict the composition for which rock-salt structure of PbTe changes into zinc-blende structure of CdTe. The dependence of the lattice parameter on Cd (Mn) content x in the mixed crystals is studied by the same methods. The obtained decrease of the lattice constant with x agrees with what is observed in both alloys. The band structures of PbTe-based ternary compounds are calculated within a tight-binding approach. To describe correctly the constituent materials new tight-binding parameterizations for PbTe and MnTe bulk crystals as well as a tight-binding description of rock-salt CdTe are proposed. For both studied ternary alloys, the calculated band gap in the L point increases with x, in qualitative agreement with photoluminescence measurements in the infrared. The results show also that in p-type Pb1-xCdxTe and Pb1-xMnxTe mixed crystals an enhancement of thermoelectrical power can be expected.

cond-mat.mtrl-sci↗

arXiv2011

Min-cuts and Shortest Cycles in Planar Graphs in O(n log log n) Time

We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This speedup is obtained through the use of dense distance graphs combined with a divide-and-conquer approach.

cs.DS↗

arXiv2011

Approximation Algorithms for Union and Intersection Covering Problems

In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least k nodes of an edge-weighted graph. Here nodes and edges represent requests and items, respectively. In this paper, we initiate the study of a new family of multi-layer covering problems. Each such problem consists of a collection of h distinct instances of a standard covering problem (layers), with the constraint that all layers share the same set of requests. We identify two main subfamilies of these problems: - in a union multi-layer problem, a request is satisfied if it is satisfied in at least one layer; - in an intersection multi-layer problem, a request is satisfied if it is satisfied in all layers. To see some natural applications, consider both generalizations of k-MST. Union k-MST can model a problem where we are asked to connect a set of users to at least one of two communication networks, e.g., a wireless and a wired network. On the other hand, intersection k-MST can formalize the problem of connecting a subset of users to both electricity and water. We present a number of hardness and approximation results for union and intersection versions of several standard optimization problems: MST, Steiner tree, set cover, facility location, TSP, and their partial covering variants.

cs.DS↗

arXiv2010

Improved Minimum Cuts and Maximum Flows in Undirected Planar Graphs

In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given vertices in O(n log log n) time. Second, we show how to achieve the same O(n log log n) bound for the problem of computing maximum flows in undirected planar graphs. To the best of our knowledge, these are the first algorithms for those two problems that break the O(n log n) barrier, which has been standing for more than 25 years. Third, we present a fully dynamic algorithm that is able to maintain information about minimum cuts and maximum flows in a plane graph (i.e., a planar graph with a fixed embedding): our algorithm is able to insert edges, delete edges and answer min-cut and max-flow queries between any pair of vertices in O(n^(2/3) log^3 n) time per operation. This result is based on a new dynamic shortest path algorithm for planar graphs which may be of independent interest. We remark that this is the first known non-trivial algorithm for min-cut and max-flow problems in a dynamic setting.

cs.DS↗

arXiv2010

Fast Approximation in Subspaces by Doubling Metric Decomposition

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees that need to be constructed for different groups of users. In our model we allow a preprocessing phase, when some information of the input graph $G=(V,E)$ is stored in a limited size data structure. Next, the data structure enables processing queries of the form ``solve problem A for an input $S\subseteq V$''. We consider problems like {\sc Steiner Forest}, {\sc Facility Location}, {\sc $k$-Median}, {\sc $k$-Center} and {\sc TSP} in the case when the graph induces a doubling metric. Our main results are data structures of near-linear size that are able to answer queries in time close to linear in $|S|$. This improves over typical worst case reuniting time of approximation algorithms in the classical setting which is $Ω(|E|)$ independently of the query size. In most cases, our approximation guarantees are arbitrarily close to those in the classical setting. Additionally, we present the first fully dynamic algorithm for the Steiner tree problem.

cs.DS↗

arXiv2010

Combinatorial Auctions with Budgets

We consider budget constrained combinatorial auctions where bidder $i$ has a private value $v_i$, a budget $b_i$, and is interested in all the items in $S_i$. The value to agent $i$ of a set of items $R$ is $|R \cap S_i| \cdot v_i$. Such auctions capture adword auctions, where advertisers offer a bid for ads in response to an advertiser-dependent set of adwords, and advertisers have budgets. It is known that even of all items are identical and all budgets are public it is not possible to be truthful and efficient. Our main result is a novel auction that runs in polynomial time, is incentive compatible, and ensures Pareto-optimality for such auctions when the valuations are private and the budgets are public knowledge. This extends the result of Dobzinski et al. (FOCS 2008) for auctions of multiple {\sl identical} items and public budgets to single-valued {\sl combinatorial} auctions with public budgets.

cs.GT↗