502 research outputs found
Truthful Mechanisms for Matching and Clustering in an Ordinal World
We study truthful mechanisms for matching and related problems in a partial
information setting, where the agents' true utilities are hidden, and the
algorithm only has access to ordinal preference information. Our model is
motivated by the fact that in many settings, agents cannot express the
numerical values of their utility for different outcomes, but are still able to
rank the outcomes in their order of preference. Specifically, we study problems
where the ground truth exists in the form of a weighted graph of agent
utilities, but the algorithm can only elicit the agents' private information in
the form of a preference ordering for each agent induced by the underlying
weights. Against this backdrop, we design truthful algorithms to approximate
the true optimum solution with respect to the hidden weights. Our techniques
yield universally truthful algorithms for a number of graph problems: a
1.76-approximation algorithm for Max-Weight Matching, 2-approximation algorithm
for Max k-matching, a 6-approximation algorithm for Densest k-subgraph, and a
2-approximation algorithm for Max Traveling Salesman as long as the hidden
weights constitute a metric. We also provide improved approximation algorithms
for such problems when the agents are not able to lie about their preferences.
Our results are the first non-trivial truthful approximation algorithms for
these problems, and indicate that in many situations, we can design robust
algorithms even when the agents may lie and only provide ordinal information
instead of precise utilities.Comment: To appear in the Proceedings of WINE 201
Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics
Simple heuristics often show a remarkable performance in practice for
optimization problems. Worst-case analysis often falls short of explaining this
performance. Because of this, "beyond worst-case analysis" of algorithms has
recently gained a lot of attention, including probabilistic analysis of
algorithms.
The instances of many optimization problems are essentially a discrete metric
space. Probabilistic analysis for such metric optimization problems has
nevertheless mostly been conducted on instances drawn from Euclidean space,
which provides a structure that is usually heavily exploited in the analysis.
However, most instances from practice are not Euclidean. Little work has been
done on metric instances drawn from other, more realistic, distributions. Some
initial results have been obtained by Bringmann et al. (Algorithmica, 2013),
who have used random shortest path metrics on complete graphs to analyze
heuristics.
The goal of this paper is to generalize these findings to non-complete
graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path
metric is constructed by drawing independent random edge weights for each edge
in the graph and setting the distance between every pair of vertices to the
length of a shortest path between them with respect to the drawn weights. For
such instances, we prove that the greedy heuristic for the minimum distance
maximum matching problem, the nearest neighbor and insertion heuristics for the
traveling salesman problem, and a trivial heuristic for the -median problem
all achieve a constant expected approximation ratio. Additionally, we show a
polynomial upper bound for the expected number of iterations of the 2-opt
heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201
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
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
The Lazy Bureaucrat Scheduling Problem
We introduce a new class of scheduling problems in which the optimization is
performed by the worker (single ``machine'') who performs the tasks. A typical
worker's objective is to minimize the amount of work he does (he is ``lazy''),
or more generally, to schedule as inefficiently (in some sense) as possible.
The worker is subject to the constraint that he must be busy when there is work
that he can do; we make this notion precise both in the preemptive and
nonpreemptive settings. The resulting class of ``perverse'' scheduling
problems, which we denote ``Lazy Bureaucrat Problems,'' gives rise to a rich
set of new questions that explore the distinction between maximization and
minimization in computing optimal schedules.Comment: 19 pages, 2 figures, Latex. To appear, Information and Computatio
The Power of Two Choices in Distributed Voting
Distributed voting is a fundamental topic in distributed computing. In pull
voting, in each step every vertex chooses a neighbour uniformly at random, and
adopts its opinion. The voting is completed when all vertices hold the same
opinion. On many graph classes including regular graphs, pull voting requires
expected steps to complete, even if initially there are only two
distinct opinions.
In this paper we consider a related process which we call two-sample voting:
every vertex chooses two random neighbours in each step. If the opinions of
these neighbours coincide, then the vertex revises its opinion according to the
chosen sample. Otherwise, it keeps its own opinion. We consider the performance
of this process in the case where two different opinions reside on vertices of
some (arbitrary) sets and , respectively. Here, is the
number of vertices of the graph.
We show that there is a constant such that if the initial imbalance
between the two opinions is ?, then with high probability two sample voting completes in a random
regular graph in steps and the initial majority opinion wins. We
also show the same performance for any regular graph, if where is the second largest eigenvalue of the transition
matrix. In the graphs we consider, standard pull voting requires
steps, and the minority can still win with probability .Comment: 22 page
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)
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
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