59,847 research outputs found
Correlation Clustering Based Coalition Formation For Multi-Robot Task Allocation
In this paper, we study the multi-robot task allocation problem where a group
of robots needs to be allocated to a set of tasks so that the tasks can be
finished optimally. One task may need more than one robot to finish it.
Therefore the robots need to form coalitions to complete these tasks.
Multi-robot coalition formation for task allocation is a well-known NP-hard
problem. To solve this problem, we use a linear-programming based graph
partitioning approach along with a region growing strategy which allocates
(near) optimal robot coalitions to tasks in a negligible amount of time. Our
proposed algorithm is fast (only taking 230 secs. for 100 robots and 10 tasks)
and it also finds a near-optimal solution (up to 97.66% of the optimal). We
have empirically demonstrated that the proposed approach in this paper always
finds a solution which is closer (up to 9.1 times) to the optimal solution than
a theoretical worst-case bound proved in an earlier work
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
Anytime Coalition Structure Generation with Worst Case Guarantees
Coalition formation is a key topic in multiagent systems. One would prefer a
coalition structure that maximizes the sum of the values of the coalitions, but
often the number of coalition structures is too large to allow exhaustive
search for the optimal one. But then, can the coalition structure found via a
partial search be guaranteed to be within a bound from optimum? We show that
none of the previous coalition structure generation algorithms can establish
any bound because they search fewer nodes than a threshold that we show
necessary for establishing a bound. We present an algorithm that establishes a
tight bound within this minimal amount of search, and show that any other
algorithm would have to search strictly more. The fraction of nodes needed to
be searched approaches zero as the number of agents grows. If additional time
remains, our anytime algorithm searches further, and establishes a
progressively lower tight bound. Surprisingly, just searching one more node
drops the bound in half. As desired, our algorithm lowers the bound rapidly
early on, and exhibits diminishing returns to computation. It also drastically
outperforms its obvious contenders. Finally, we show how to distribute the
desired search across self-interested manipulative agents
Coalition structure generation over graphs
We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) ā R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members ā that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ā„ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph
Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem
A recent work of Harn and Fuyou presents the first multilevel (disjunctive)
threshold secret sharing scheme based on the Chinese Remainder Theorem. In this
work, we first show that the proposed method is not secure and also fails to
work with a certain natural setting of the threshold values on compartments. We
then propose a secure scheme that works for all threshold settings. In this
scheme, we employ a refined version of Asmuth-Bloom secret sharing with a
special and generic Asmuth-Bloom sequence called the {\it anchor sequence}.
Based on this idea, we also propose the first multilevel conjunctive threshold
secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we
discuss how the proposed schemes can be used for multilevel threshold function
sharing by employing it in a threshold RSA cryptosystem as an example
A hybrid algorithm for coalition structure generation
The current state-of-the-art algorithm for optimal coalition structure generation is IDP-IPāan algorithm that combines IDP (a dynamic programming algorithm due to Rahwan and Jennings, 2008b) with IP (a tree-search algorithm due to Rahwan et al., 2009). In this paper we analyse IDP-IP, highlight its limitations, and then develop a new approach for combining IDP with IP that overcomes these limitations
Socially Trusted Collaborative Edge Computing in Ultra Dense Networks
Small cell base stations (SBSs) endowed with cloud-like computing
capabilities are considered as a key enabler of edge computing (EC), which
provides ultra-low latency and location-awareness for a variety of emerging
mobile applications and the Internet of Things. However, due to the limited
computation resources of an individual SBS, providing computation services of
high quality to its users faces significant challenges when it is overloaded
with an excessive amount of computation workload. In this paper, we propose
collaborative edge computing among SBSs by forming SBS coalitions to share
computation resources with each other, thereby accommodating more computation
workload in the edge system and reducing reliance on the remote cloud. A novel
SBS coalition formation algorithm is developed based on the coalitional game
theory to cope with various new challenges in small-cell-based edge systems,
including the co-provisioning of radio access and computing services,
cooperation incentives, and potential security risks. To address these
challenges, the proposed method (1) allows collaboration at both the user-SBS
association stage and the SBS peer offloading stage by exploiting the ultra
dense deployment of SBSs, (2) develops a payment-based incentive mechanism that
implements proportionally fair utility division to form stable SBS coalitions,
and (3) builds a social trust network for managing security risks among SBSs
due to collaboration. Systematic simulations in practical scenarios are carried
out to evaluate the efficacy and performance of the proposed method, which
shows that tremendous edge computing performance improvement can be achieved.Comment: arXiv admin note: text overlap with arXiv:1010.4501 by other author
Cooperative Games with Overlapping Coalitions
In the usual models of cooperative game theory, the outcome of a coalition
formation process is either the grand coalition or a coalition structure that
consists of disjoint coalitions. However, in many domains where coalitions are
associated with tasks, an agent may be involved in executing more than one
task, and thus may distribute his resources among several coalitions. To tackle
such scenarios, we introduce a model for cooperative games with overlapping
coalitions--or overlapping coalition formation (OCF) games. We then explore the
issue of stability in this setting. In particular, we introduce a notion of the
core, which generalizes the corresponding notion in the traditional
(non-overlapping) scenario. Then, under some quite general conditions, we
characterize the elements of the core, and show that any element of the core
maximizes the social welfare. We also introduce a concept of balancedness for
overlapping coalitional games, and use it to characterize coalition structures
that can be extended to elements of the core. Finally, we generalize the notion
of convexity to our setting, and show that under some natural assumptions
convex games have a non-empty core. Moreover, we introduce two alternative
notions of stability in OCF that allow a wider range of deviations, and explore
the relationships among the corresponding definitions of the core, as well as
the classic (non-overlapping) core and the Aubin core. We illustrate the
general properties of the three cores, and also study them from a computational
perspective, thus obtaining additional insights into their fundamental
structure
Complexity of Determining Nonemptiness of the Core
Coalition formation is a key problem in automated negotiation among
self-interested agents, and other multiagent applications. A coalition of
agents can sometimes accomplish things that the individual agents cannot, or
can do things more efficiently. However, motivating the agents to abide to a
solution requires careful analysis: only some of the solutions are stable in
the sense that no group of agents is motivated to break off and form a new
coalition. This constraint has been studied extensively in cooperative game
theory. However, the computational questions around this constraint have
received less attention. When it comes to coalition formation among software
agents (that represent real-world parties), these questions become increasingly
explicit.
In this paper we define a concise general representation for games in
characteristic form that relies on superadditivity, and show that it allows for
efficient checking of whether a given outcome is in the core. We then show that
determining whether the core is nonempty is -complete both with
and without transferable utility. We demonstrate that what makes the problem
hard in both cases is determining the collaborative possibilities (the set of
outcomes possible for the grand coalition), by showing that if these are given,
the problem becomes tractable in both cases. However, we then demonstrate that
for a hybrid version of the problem, where utility transfer is possible only
within the grand coalition, the problem remains -complete even
when the collaborative possibilities are given
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