577 research outputs found
On the Approximability of Digraph Ordering
Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute
a labeling maximizing the number of forward edges, i.e.
edges (u,v) such that (u) < (v). For different values of k, this
reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work
studies the approximability of Max-k-Ordering and its generalizations,
motivated by their applications to job scheduling with soft precedence
constraints. We give an LP rounding based 2-approximation algorithm for
Max-k-Ordering for any k={2,..., n}, improving on the known
2k/(k-1)-approximation obtained via random assignment. The tightness of this
rounding is shown by proving that for any k={2,..., n} and constant
, Max-k-Ordering has an LP integrality gap of 2 -
for rounds of the
Sherali-Adams hierarchy.
A further generalization of Max-k-Ordering is the restricted maximum acyclic
subgraph problem or RMAS, where each vertex v has a finite set of allowable
labels . We prove an LP rounding based
approximation for it, improving on the
approximation recently given by Grandoni et al.
(Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact,
our approximation algorithm also works for a general version where the
objective counts the edges which go forward by at least a positive offset
specific to each edge.
The minimization formulation of digraph ordering is DAG edge deletion or
DED(k), which requires deleting the minimum number of edges from an n-vertex
directed acyclic graph (DAG) to remove all paths of length k. We show that
both, the LP relaxation and a local ratio approach for DED(k) yield
k-approximation for any .Comment: 21 pages, Conference version to appear in ESA 201
All quantum states useful for teleportation are nonlocal resources
Understanding the relation between the different forms of inseparability in
quantum mechanics is a longstanding problem in the foundations of quantum
theory and has implications for quantum information processing. Here we make
progress in this direction by establishing a direct link between quantum
teleportation and Bell nonlocality. In particular, we show that all entangled
states which are useful for teleportation are nonlocal resources, i.e. lead to
deterministic violation of Bell's inequality. Our result exploits the
phenomenon of super-activation of quantum nonlocality, recently proved by
Palazuelos, and suggests that the latter might in fact be generic.Comment: 4 pages. v2: Title and abstract changed, presentation improved,
references updated, same result
Hitting Diamonds and Growing Cacti
We consider the following NP-hard problem: in a weighted graph, find a
minimum cost set of vertices whose removal leaves a graph in which no two
cycles share an edge. We obtain a constant-factor approximation algorithm,
based on the primal-dual method. Moreover, we show that the integrality gap of
the natural LP relaxation of the problem is \Theta(\log n), where n denotes the
number of vertices in the graph.Comment: v2: several minor changes
A Hypergraph Dictatorship Test with Perfect Completeness
A hypergraph dictatorship test is first introduced by Samorodnitsky and
Trevisan and serves as a key component in their unique games based \PCP
construction. Such a test has oracle access to a collection of functions and
determines whether all the functions are the same dictatorship, or all their
low degree influences are Their test makes queries and has
amortized query complexity but has an inherent loss of
perfect completeness. In this paper we give an adaptive hypergraph dictatorship
test that achieves both perfect completeness and amortized query complexity
.Comment: Some minor correction
Scheduling over Scenarios on Two Machines
We consider scheduling problems over scenarios where the goal is to find a
single assignment of the jobs to the machines which performs well over all
possible scenarios. Each scenario is a subset of jobs that must be executed in
that scenario and all scenarios are given explicitly. The two objectives that
we consider are minimizing the maximum makespan over all scenarios and
minimizing the sum of the makespans of all scenarios. For both versions, we
give several approximation algorithms and lower bounds on their
approximability. With this research into optimization problems over scenarios,
we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at
link.springer.co
Structural Optimization Using the Newton Modified Barrier Method
The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program
Finding Connected Dense -Subgraphs
Given a connected graph on vertices and a positive integer ,
a subgraph of on vertices is called a -subgraph in . We design
combinatorial approximation algorithms for finding a connected -subgraph in
such that its density is at least a factor
of the density of the densest -subgraph
in (which is not necessarily connected). These particularly provide the
first non-trivial approximations for the densest connected -subgraph problem
on general graphs
DEVELOPMENT OF A DEVICE TO MEASURE THE BLADE TIP CLEARANCE OF AN AXIAL COMPRESSOR
Axial compressors, used in gas turbines, jet engines and also small scale power plants, are rotating, airfoil based compressors in which the working fluid flows parallel to the axis of rotation. There has been continuous struggle to maximize the efficiency of these compressors. One of the many ways to achieve the same is to minimize the tip clearance i.e. to reduce the distance between the blade tip and the housing. Experiments need to be conducted to measure the changes in the tip clearance while the compressor is operating. Conventional devices to measure this tip clearance have proven to be costly if a small scale application is under consideration. Our aim in this project is to develop a device which will measure the blade tip clearance of an axial flow compressor economically. The literature review, development of the device, its working and results will be discussed in this paper
- …