2,481 research outputs found
FPT-algorithms for some problems related to integer programming
In this paper, we present FPT-algorithms for special cases of the shortest
lattice vector, integer linear programming, and simplex width computation
problems, when matrices included in the problems' formulations are near square.
The parameter is the maximum absolute value of rank minors of the corresponding
matrices. Additionally, we present FPT-algorithms with respect to the same
parameter for the problems, when the matrices have no singular rank
sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author:
some minor corrections has been don
Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges
Computational Social Choice is an interdisciplinary research area involving
Economics, Political Science, and Social Science on the one side, and
Mathematics and Computer Science (including Artificial Intelligence and
Multiagent Systems) on the other side. Typical computational problems studied
in this field include the vulnerability of voting procedures against attacks,
or preference aggregation in multi-agent systems. Parameterized Algorithmics is
a subfield of Theoretical Computer Science seeking to exploit meaningful
problem-specific parameters in order to identify tractable special cases of in
general computationally hard problems. In this paper, we propose nine of our
favorite research challenges concerning the parameterized complexity of
problems appearing in this context
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 Complexity of Problems in Coalitional Resource Games
Coalition formation is a key topic in multi-agent systems. Coalitions enable
agents to achieve goals that they may not have been able to achieve on their
own. Previous work has shown problems in coalitional games to be
computationally hard. Wooldridge and Dunne (Artificial Intelligence 2006)
studied the classical computational complexity of several natural decision
problems in Coalitional Resource Games (CRG) - games in which each agent is
endowed with a set of resources and coalitions can bring about a set of goals
if they are collectively endowed with the necessary amount of resources. The
input of coalitional resource games bundles together several elements, e.g.,
the agent set Ag, the goal set G, the resource set R, etc. Shrot, Aumann and
Kraus (AAMAS 2009) examine coalition formation problems in the CRG model using
the theory of Parameterized Complexity. Their refined analysis shows that not
all parts of input act equal - some instances of the problem are indeed
tractable while others still remain intractable.
We answer an important question left open by Shrot, Aumann and Kraus by
showing that the SC Problem (checking whether a Coalition is Successful) is
W[1]-hard when parameterized by the size of the coalition. Then via a single
theme of reduction from SC, we are able to show that various problems related
to resources, resource bounds and resource conflicts introduced by Wooldridge
et al are 1. W[1]-hard or co-W[1]-hard when parameterized by the size of the
coalition. 2. para-NP-hard or co-para-NP-hard when parameterized by |R|. 3. FPT
when parameterized by either |G| or |Ag|+|R|.Comment: This is the full version of a paper that will appear in the
proceedings of AAAI 201
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