462 research outputs found
Maximum st-flow in directed planar graphs via shortest paths
Minimum cuts have been closely related to shortest paths in planar graphs via
planar duality - so long as the graphs are undirected. Even maximum flows are
closely related to shortest paths for the same reason - so long as the source
and the sink are on a common face. In this paper, we give a correspondence
between maximum flows and shortest paths via duality in directed planar graphs
with no constraints on the source and sink. We believe this a promising avenue
for developing algorithms that are more practical than the current
asymptotically best algorithms for maximum st-flow.Comment: 20 pages, 4 figures. Short version to be published in proceedings of
IWOCA'1
On Approximating Restricted Cycle Covers
A cycle cover of a graph is a set of cycles such that every vertex is part of
exactly one cycle. An L-cycle cover is a cycle cover in which the length of
every cycle is in the set L. The weight of a cycle cover of an edge-weighted
graph is the sum of the weights of its edges.
We come close to settling the complexity and approximability of computing
L-cycle covers. On the one hand, we show that for almost all L, computing
L-cycle covers of maximum weight in directed and undirected graphs is APX-hard
and NP-hard. Most of our hardness results hold even if the edge weights are
restricted to zero and one.
On the other hand, we show that the problem of computing L-cycle covers of
maximum weight can be approximated within a factor of 2 for undirected graphs
and within a factor of 8/3 in the case of directed graphs. This holds for
arbitrary sets L.Comment: To appear in SIAM Journal on Computing. Minor change
EFFECT OF GENETIC AND ENVIRONMENTAL FACTORS ON SEX RATIO IN CROSSBRED PIGS
The study was initiated with an idea to investigate few genetic and environmental factors that affect sex ratio of Khasi local and their different crossbreds with Hampshire pigs. Individual data were collected of pure Khasi local and its crossbred with 50, 75 and 87.5 % Hampshire inheritance in different seasons like rainy (July to October), summer (March-June) and winter (Nov- Feb). The sex ratio for Khasi local crossbred with 50, 75 and 87.5 % Hampshire inheritance was 1.21 ± 0.16, 1.32 ± 0.16, 1.48 ± 0.16 an 1.32 ± 0.16 respectively with an overall mean sex ratio 1.38 ± 0.16,
whereas, the sex ratio for spring, rainy and winter season was 1.31 ± 0.17, 1.29 ± 0.16 and 1.32 ± 0.15, respectively. Similarly, the sex ratio for larger litters and smaller litters was 1.40 ± 0.13 and 1.45 ± 0.13 respectively. This study concludes that crossbreds at different levels of inheritance, season and litter size had no effect on sex ratio
The complexity of the Pk partition problem and related problems in bipartite graphs
International audienceIn this paper, we continue the investigation made in [MT05] about the approximability of Pk partition problems, but focusing here on their complexity. Precisely, we aim at designing the frontier between polynomial and NP-complete versions of the Pk partition problem in bipartite graphs, according to both the constant k and the maximum degree of the input graph. We actually extend the obtained results to more general classes of problems, namely, the minimum k-path partition problem and the maximum Pk packing problem. Moreover, we propose some simple approximation algorithms for those problems
A -Vertex Kernel for Maximum Internal Spanning Tree
We consider the parameterized version of the maximum internal spanning tree
problem, which, given an -vertex graph and a parameter , asks for a
spanning tree with at least internal vertices. Fomin et al. [J. Comput.
System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a
simple application of this rule is sufficient to yield a -vertex kernel.
Here we propose a novel way to use the same reduction rule, resulting in an
improved -vertex kernel. Our algorithm applies first a greedy procedure
consisting of a sequence of local exchange operations, which ends with a
local-optimal spanning tree, and then uses this special tree to find a
reducible structure. As a corollary of our kernel, we obtain a deterministic
algorithm for the problem running in time
Probabilistic Analysis of Facility Location on Random Shortest Path Metrics
The facility location problem is an NP-hard optimization problem. Therefore,
approximation algorithms are often used to solve large instances. Such
algorithms often perform much better than worst-case analysis suggests.
Therefore, probabilistic analysis is a widely used tool to analyze such
algorithms. Most research on probabilistic analysis of NP-hard optimization
problems involving metric spaces, such as the facility location problem, has
been focused on Euclidean instances, and also instances with independent
(random) edge lengths, which are non-metric, have been researched. We would
like to extend this knowledge to other, more general, metrics.
We investigate the facility location problem using random shortest path
metrics. We analyze some probabilistic properties for a simple greedy heuristic
which gives a solution to the facility location problem: opening the
cheapest facilities (with only depending on the facility opening
costs). If the facility opening costs are such that is not too large,
then we show that this heuristic is asymptotically optimal. On the other hand,
for large values of , the analysis becomes more difficult, and we
provide a closed-form expression as upper bound for the expected approximation
ratio. In the special case where all facility opening costs are equal this
closed-form expression reduces to or or even
if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201
On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint
In the problem of minimum connected dominating set with routing cost
constraint, we are given a graph , and the goal is to find the
smallest connected dominating set of such that, for any two
non-adjacent vertices and in , the number of internal nodes on the
shortest path between and in the subgraph of induced by is at most times that in . For general graphs, the only
known previous approximability result is an -approximation algorithm
() for by Ding et al. For any constant , we
give an -approximation
algorithm. When , we give an -approximation
algorithm. Finally, we prove that, when , unless , for any constant , the problem admits no
polynomial-time -approximation algorithm, improving
upon the bound by Du et al. (albeit under a stronger hardness
assumption)
Discrete Convex Functions on Graphs and Their Algorithmic Applications
The present article is an exposition of a theory of discrete convex functions
on certain graph structures, developed by the author in recent years. This
theory is a spin-off of discrete convex analysis by Murota, and is motivated by
combinatorial dualities in multiflow problems and the complexity classification
of facility location problems on graphs. We outline the theory and algorithmic
applications in combinatorial optimization problems
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