84 research outputs found
Ascending auctions and Walrasian equilibrium
We present a family of submodular valuation classes that generalizes gross
substitute. We show that Walrasian equilibrium always exist for one class in
this family, and there is a natural ascending auction which finds it. We prove
some new structural properties on gross-substitute auctions which, in turn,
show that the known ascending auctions for this class (Gul-Stacchetti and
Ausbel) are, in fact, identical. We generalize these two auctions, and provide
a simple proof that they terminate in a Walrasian equilibrium
No Ascending Auction can find Equilibrium for SubModular valuations
We show that no efficient ascending auction can guarantee to find even a
minimal envy-free price vector if all valuations are submodular, assuming a
basic complexity theory's assumption.Comment: arXiv admin note: text overlap with arXiv:1301.115
Parameterized Approximation Schemes using Graph Widths
Combining the techniques of approximation algorithms and parameterized
complexity has long been considered a promising research area, but relatively
few results are currently known. In this paper we study the parameterized
approximability of a number of problems which are known to be hard to solve
exactly when parameterized by treewidth or clique-width. Our main contribution
is to present a natural randomized rounding technique that extends well-known
ideas and can be used for both of these widths. Applying this very generic
technique we obtain approximation schemes for a number of problems, evading
both polynomial-time inapproximability and parameterized intractability bounds
Parameterized Inapproximability of Target Set Selection and Generalizations
In this paper, we consider the Target Set Selection problem: given a graph
and a threshold value for any vertex of the graph, find a minimum
size vertex-subset to "activate" s.t. all the vertices of the graph are
activated at the end of the propagation process. A vertex is activated
during the propagation process if at least of its neighbors are
activated. This problem models several practical issues like faults in
distributed networks or word-to-mouth recommendations in social networks. We
show that for any functions and this problem cannot be approximated
within a factor of in time, unless FPT = W[P],
even for restricted thresholds (namely constant and majority thresholds). We
also study the cardinality constraint maximization and minimization versions of
the problem for which we prove similar hardness results
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that
generalizes existing schemata recently proposed in the literature. In our
model, agents change behaviors/opinions on the basis of information collected
from their neighbors in a time interval of bounded size whereas agents are
assumed to have unbounded memory in previously studied scenarios. In our
mathematical framework, one is given a network , an integer value
for each node , and a time window size . The goal is to
determine a small set of nodes (target set) that influences the whole graph.
The spread of influence proceeds in rounds as follows: initially all nodes in
the target set are influenced; subsequently, in each round, any uninfluenced
node becomes influenced if the number of its neighbors that have been
influenced in the previous rounds is greater than or equal to .
We prove that the problem of finding a minimum cardinality target set that
influences the whole network is hard to approximate within a
polylogarithmic factor. On the positive side, we design exact polynomial time
algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared
in: Proceedings of 20th International Colloquium on Structural Information
and Communication Complexity (Sirocco 2013), Lectures Notes in Computer
Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201
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