3,025 research outputs found
Uniform Partition in Population Protocol Model Under Weak Fairness
We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k=2 (called uniform bipartition), a previous work clarified space complexity under various assumptions: 1) an initialized base station (BS) or no BS, 2) weak or global fairness, 3) designated or arbitrary initial states of agents, and 4) symmetric or asymmetric protocols, except for the setting that agents execute a protocol from arbitrary initial states under weak fairness in the model with an initialized base station. In this paper, we clarify the space complexity for this remaining setting. In this setting, we prove that P states are necessary and sufficient to realize asymmetric protocols, and that P+1 states are necessary and sufficient to realize symmetric protocols, where P is the known upper bound of the number of agents. From these results and the previous work, we have clarified the solvability of the uniform bipartition for each combination of assumptions. Additionally, we newly consider an assumption on a model of a non-initialized BS and clarify solvability and space complexity in the assumption. Moreover, the results in this paper can be applied to the case that k is an arbitrary integer (called uniform k-partition)
Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs
In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of arbitrary communication graphs. As a result, we investigate the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight
Constant-Space Population Protocols for Uniform Bipartition
In this paper, we consider a uniform bipartition problem in a population protocol model. The goal of the uniform bipartition problem is to divide a population into two groups of the same size. We study the problem under various assumptions: 1) a population with or without a base station, 2) weak or global fairness, 3) symmetric or asymmetric protocols, and 4) designated or arbitrary initial states. As a result, we completely clarify constant-space solvability of the uniform bipartition problem and, if solvable, propose space-optimal protocols
Simple and Efficient Local Codes for Distributed Stable Network Construction
In this work, we study protocols so that populations of distributed processes
can construct networks. In order to highlight the basic principles of
distributed network construction we keep the model minimal in all respects. In
particular, we assume finite-state processes that all begin from the same
initial state and all execute the same protocol (i.e. the system is
homogeneous). Moreover, we assume pairwise interactions between the processes
that are scheduled by an adversary. The only constraint on the adversary
scheduler is that it must be fair. In order to allow processes to construct
networks, we let them activate and deactivate their pairwise connections. When
two processes interact, the protocol takes as input the states of the processes
and the state of the their connection and updates all of them. Initially all
connections are inactive and the goal is for the processes, after interacting
and activating/deactivating connections for a while, to end up with a desired
stable network. We give protocols (optimal in some cases) and lower bounds for
several basic network construction problems such as spanning line, spanning
ring, spanning star, and regular network. We provide proofs of correctness for
all of our protocols and analyze the expected time to convergence of most of
them under a uniform random scheduler that selects the next pair of interacting
processes uniformly at random from all such pairs. Finally, we prove several
universality results by presenting generic protocols that are capable of
simulating a Turing Machine (TM) and exploiting it in order to construct a
large class of networks.Comment: 43 pages, 7 figure
Redividing the Cake
A heterogeneous resource, such as a land-estate, is already divided among
several agents in an unfair way. It should be re-divided among the agents in a
way that balances fairness with ownership rights. We present re-division
protocols that attain various trade-off points between fairness and ownership
rights, in various settings differing in the geometric constraints on the
allotments: (a) no geometric constraints; (b) connectivity --- the cake is a
one-dimensional interval and each piece must be a contiguous interval; (c)
rectangularity --- the cake is a two-dimensional rectangle or rectilinear
polygon and the pieces should be rectangles; (d) convexity --- the cake is a
two-dimensional convex polygon and the pieces should be convex.
Our re-division protocols have implications on another problem: the
price-of-fairness --- the loss of social welfare caused by fairness
requirements. Each protocol implies an upper bound on the price-of-fairness
with the respective geometric constraints.Comment: Extended IJCAI 2018 version. Previous name: "How to Re-Divide a Cake
Fairly
Democratic Fair Allocation of Indivisible Goods
We study the problem of fairly allocating indivisible goods to groups of
agents. Agents in the same group share the same set of goods even though they
may have different preferences. Previous work has focused on unanimous
fairness, in which all agents in each group must agree that their group's share
is fair. Under this strict requirement, fair allocations exist only for small
groups. We introduce the concept of democratic fairness, which aims to satisfy
a certain fraction of the agents in each group. This concept is better suited
to large groups such as cities or countries. We present protocols for
democratic fair allocation among two or more arbitrarily large groups of agents
with monotonic, additive, or binary valuations. For two groups with arbitrary
monotonic valuations, we give an efficient protocol that guarantees
envy-freeness up to one good for at least of the agents in each group,
and prove that the fraction is optimal. We also present other protocols
that make weaker fairness guarantees to more agents in each group, or to more
groups. Our protocols combine techniques from different fields, including
combinatorial game theory, cake cutting, and voting.Comment: Appears in the 27th International Joint Conference on Artificial
Intelligence and the 23rd European Conference on Artificial Intelligence
(IJCAI-ECAI), 201
On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions
This paper studies the (discrete) chemical reaction network (CRN) computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a stochastic scheduler that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an adversarial scheduler whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes "idealized conditions" that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the runtime of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption?
The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short rounds and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks
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