1,670 research outputs found
Computing maximum matchings in temporal graphs.
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms
Computing maximum matchings in temporal graphs
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms
Relative multiplexing for minimizing switching in linear-optical quantum computing
Many existing schemes for linear-optical quantum computing (LOQC) depend on
multiplexing (MUX), which uses dynamic routing to enable near-deterministic
gates and sources to be constructed using heralded, probabilistic primitives.
MUXing accounts for the overwhelming majority of active switching demands in
current LOQC architectures. In this manuscript, we introduce relative
multiplexing (RMUX), a general-purpose optimization which can dramatically
reduce the active switching requirements for MUX in LOQC, and thereby reduce
hardware complexity and energy consumption, as well as relaxing demands on
performance for various photonic components. We discuss the application of RMUX
to the generation of entangled states from probabilistic single-photon sources,
and argue that an order of magnitude improvement in the rate of generation of
Bell states can be achieved. In addition, we apply RMUX to the proposal for
percolation of a 3D cluster state in [PRL 115, 020502 (2015)], and we find that
RMUX allows a 2.4x increase in loss tolerance for this architecture.Comment: Published version, New Journal of Physics, Volume 19, June 201
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