15 research outputs found
A simple and effective algorithm for the maximum happy vertices problem
In a recent paper, a solution approach to the Maximum Happy Vertices Problem has
been proposed. The approach is based on a constructive heuristic improved by a
matheuristic local search phase. We propose a new procedure able to outperform
the previous solution algorithm both in terms of solution quality and computational
time. Our approach is based on simple ingredients implying as starting solution gen-
erator an approximation algorithm and as an improving phase a new matheuristic
local search. The procedure is then extended to a multi-start configuration, able to
further improve the solution quality at the cost of an acceptable increase in compu-
tational time
Parameterized Complexity of Maximum Happy Set and Densest k-Subgraph
We present fixed-parameter tractable (FPT) algorithms for two problems,
Maximum Happy Set (MaxHS) and Maximum Edge Happy Set (MaxEHS)--also known as
Densest k-Subgraph. Given a graph and an integer , MaxHS asks for a set
of vertices such that the number of with
respect to is maximized, where a vertex is happy if and all its
neighbors are in . We show that MaxHS can be solved in time
and , where and denote the
and the of , respectively.
This resolves the open questions posed in literature. The MaxEHS problem is an
edge-variant of MaxHS, where we maximize the number of ,
the edges whose endpoints are in . In this paper we show that MaxEHS can be
solved in time and
, where
and denote the
and the of , respectively, and is
some computable function. This result implies that MaxEHS is also
fixed-parameter tractable by
Maximizing Happiness in Graphs of Bounded Clique-Width
Clique-width is one of the most important parameters that describes
structural complexity of a graph. Probably, only treewidth is more studied
graph width parameter. In this paper we study how clique-width influences the
complexity of the Maximum Happy Vertices (MHV) and Maximum Happy Edges (MHE)
problems. We answer a question of Choudhari and Reddy '18 about
parameterization by the distance to threshold graphs by showing that MHE is
NP-complete on threshold graphs. Hence, it is not even in XP when parameterized
by clique-width, since threshold graphs have clique-width at most two. As a
complement for this result we provide a algorithm for MHE, where is the number of colors
and is the clique-width of the input graph. We also
construct an FPT algorithm for MHV with running time
, where is the
number of colors in the input. Additionally, we show
algorithm for MHV on interval graphs.Comment: Accepted to LATIN 202
Unpacking How Decentralized Autonomous Organizations (DAOs) Work in Practice
Decentralized Autonomous Organizations (DAOs) have emerged as a novel way to
coordinate a group of (pseudonymous) entities towards a shared vision (e.g.,
promoting sustainability), utilizing self-executing smart contracts on
blockchains to support decentralized governance and decision-making. In just a
few years, over 4,000 DAOs have been launched in various domains, such as
investment, education, health, and research. Despite such rapid growth and
diversity, it is unclear how these DAOs actually work in practice and to what
extent they are effective in achieving their goals. Given this, we aim to
unpack how (well) DAOs work in practice. We conducted an in-depth analysis of a
diverse set of 10 DAOs of various categories and smart contracts, leveraging
on-chain (e.g., voting results) and off-chain data (e.g., community
discussions) as well as our interviews with DAO organizers/members.
Specifically, we defined metrics to characterize key aspects of DAOs, such as
the degrees of decentralization and autonomy. We observed CompoundDAO,
AssangeDAO, Bankless, and Krausehouse having poor decentralization in voting,
while decentralization has improved over time for one-person-one-vote DAOs
(e.g., Proof of Humanity). Moreover, the degree of autonomy varies among DAOs,
with some (e.g., Compound and Krausehouse) relying more on third parties than
others. Lastly, we offer a set of design implications for future DAO systems
based on our findings
A heuristic algorithm using tree decompositions for the maximum happy vertices problem
We propose a new methodology to develop heuristic algorithms using tree
decompositions. Traditionally, such algorithms construct an optimal solution of
the given problem instance through a dynamic programming approach. We modify
this procedure by introducing a parameter that dictates the number of
dynamic programming states to consider. We drop the exactness guarantee in
favour of a shorter running time. However, if is large enough such that all
valid states are considered, our heuristic algorithm proves optimality of the
constructed solution. In particular, we implement a heuristic algorithm for the
Maximum Happy Vertices problem using this approach. Our algorithm more
efficiently constructs optimal solutions compared to the exact algorithm for
graphs of bounded treewidth. Furthermore, our algorithm constructs higher
quality solutions than state-of-the-art heuristic algorithms Greedy-MHV and
Growth-MHV for instances of which at least 40\% of the vertices are initially
coloured, at the cost of a larger running time.Comment: 31 pages, to appear in Journal of Heuristic