168 research outputs found
Multivariate Analyis of Swap Bribery
We consider the computational complexity of a problem modeling bribery in the
context of voting systems. In the scenario of Swap Bribery, each voter assigns
a certain price for swapping the positions of two consecutive candidates in his
preference ranking. The question is whether it is possible, without exceeding a
given budget, to bribe the voters in a way that the preferred candidate wins in
the election. We initiate a parameterized and multivariate complexity analysis
of Swap Bribery, focusing on the case of k-approval. We investigate how
different cost functions affect the computational complexity of the problem. We
identify a special case of k-approval for which the problem can be solved in
polynomial time, whereas we prove NP-hardness for a slightly more general
scenario. We obtain fixed-parameter tractability as well as W[1]-hardness
results for certain natural parameters.Comment: 20 pages. Conference version published at IPEC 201
Swap Bribery
In voting theory, bribery is a form of manipulative behavior in which an
external actor (the briber) offers to pay the voters to change their votes in
order to get her preferred candidate elected. We investigate a model of bribery
where the price of each vote depends on the amount of change that the voter is
asked to implement. Specifically, in our model the briber can change a voter's
preference list by paying for a sequence of swaps of consecutive candidates.
Each swap may have a different price; the price of a bribery is the sum of the
prices of all swaps that it involves. We prove complexity results for this
model, which we call swap bribery, for a broad class of election systems,
including variants of approval and k-approval, Borda, Copeland, and maximin.Comment: 17 page
Parameterizing by the Number of Numbers
The usefulness of parameterized algorithmics has often depended on what
Niedermeier has called, "the art of problem parameterization". In this paper we
introduce and explore a novel but general form of parameterization: the number
of numbers. Several classic numerical problems, such as Subset Sum, Partition,
3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with
Target Sums, have multisets of integers as input. We initiate the study of
parameterizing these problems by the number of distinct integers in the input.
We rely on an FPT result for ILPF to show that all the above-mentioned problems
are fixed-parameter tractable when parameterized in this way. In various
applied settings, problem inputs often consist in part of multisets of integers
or multisets of weighted objects (such as edges in a graph, or jobs to be
scheduled). Such number-of-numbers parameterized problems often reduce to
subproblems about transition systems of various kinds, parameterized by the
size of the system description. We consider several core problems of this kind
relevant to number-of-numbers parameterization. Our main hardness result
considers the problem: given a non-deterministic Mealy machine M (a finite
state automaton outputting a letter on each transition), an input word x, and a
census requirement c for the output word specifying how many times each letter
of the output alphabet should be written, decide whether there exists a
computation of M reading x that outputs a word y that meets the requirement c.
We show that this problem is hard for W[1]. If the question is whether there
exists an input word x such that a computation of M on x outputs a word that
meets c, the problem becomes fixed-parameter tractable
Hitting forbidden subgraphs in graphs of bounded treewidth
We study the complexity of a generic hitting problem H-Subgraph Hitting,
where given a fixed pattern graph and an input graph , the task is to
find a set of minimum size that hits all subgraphs of
isomorphic to . In the colorful variant of the problem, each vertex of
is precolored with some color from and we require to hit only
-subgraphs with matching colors. Standard techniques shows that for every
fixed , the problem is fixed-parameter tractable parameterized by the
treewidth of ; however, it is not clear how exactly the running time should
depend on treewidth. For the colorful variant, we demonstrate matching upper
and lower bounds showing that the dependence of the running time on treewidth
of is tightly governed by , the maximum size of a minimal vertex
separator in . That is, we show for every fixed that, on a graph of
treewidth , the colorful problem can be solved in time
, but cannot be solved in time
, assuming the Exponential Time
Hypothesis (ETH). Furthermore, we give some preliminary results showing that,
in the absence of colors, the parameterized complexity landscape of H-Subgraph
Hitting is much richer.Comment: A full version of a paper presented at MFCS 201
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
Combinatorial Voter Control in Elections
Voter control problems model situations such as an external agent trying to
affect the result of an election by adding voters, for example by convincing
some voters to vote who would otherwise not attend the election. Traditionally,
voters are added one at a time, with the goal of making a distinguished
alternative win by adding a minimum number of voters. In this paper, we
initiate the study of combinatorial variants of control by adding voters: In
our setting, when we choose to add a voter~, we also have to add a whole
bundle of voters associated with . We study the computational
complexity of this problem for two of the most basic voting rules, namely the
Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
Mangarara Formation: exhumed remnants of a middle Miocene, temperate carbonate, submarine channel-fan system on the eastern margin of Taranaki Basin, New Zealand
The middle Miocene Mangarara Formation is a thin (1â60 m), laterally discontinuous unit of moderately to highly calcareous (40â90%) facies of sandy to pure limestone, bioclastic sandstone, and conglomerate that crops out in a few valleys in North Taranaki across the transition from King Country Basin into offshore Taranaki Basin. The unit occurs within hemipelagic (slope) mudstone of Manganui Formation, is stratigraphically associated with redeposited sandstone of Moki Formation, and is overlain by redeposited volcaniclastic sandstone of Mohakatino Formation. The calcareous facies of the Mangarara Formation are interpreted to be mainly mass-emplaced deposits having channelised and sheet-like geometries, sedimentary structures supportive of redeposition, mixed environment fossil associations, and stratigraphic enclosure within bathyal mudrocks and flysch. The carbonate component of the deposits consists mainly of bivalves, larger benthic foraminifers (especially Amphistegina), coralline red algae including rhodoliths (Lithothamnion and Mesophyllum), and bryozoans, a warm-temperate, shallow marine skeletal association. While sediment derivation was partly from an eastern contemporary shelf, the bulk of the skeletal carbonate is inferred to have been sourced from shoal carbonate factories around and upon isolated basement highs (Patea-Tongaporutu High) to the south. The Mangarara sediments were redeposited within slope gullies and broad open submarine channels and lobes in the vicinity of the channel-lobe transition zone of a submarine fan system. Different phases of sediment transport and deposition (lateral-accretion and aggradation stages) are identified in the channel infilling. Dual fan systems likely co-existed, one dominating and predominantly siliciclastic in nature (Moki Formation), and the other infrequent and involving the temperate calcareous deposits of Mangarara Formation. The Mangarara Formation is an outcrop analogue for middle Miocene-age carbonate slope-fan deposits elsewhere in subsurface Taranaki Basin, New Zealand
Finding and counting vertex-colored subtrees
The problems studied in this article originate from the Graph Motif problem
introduced by Lacroix et al. in the context of biological networks. The problem
is to decide if a vertex-colored graph has a connected subgraph whose colors
equal a given multiset of colors . It is a graph pattern-matching problem
variant, where the structure of the occurrence of the pattern is not of
interest but the only requirement is the connectedness. Using an algebraic
framework recently introduced by Koutis et al., we obtain new FPT algorithms
for Graph Motif and variants, with improved running times. We also obtain
results on the counting versions of this problem, proving that the counting
problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two
colors. Finally, we present an experimental evaluation of this approach on real
datasets, showing that its performance compares favorably with existing
software.Comment: Conference version in International Symposium on Mathematical
Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal
Version in Algorithmic
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