4,889 research outputs found
Power and Channel Allocation for Non-orthogonal Multiple Access in 5G Systems: Tractability and Computation
Network capacity calls for significant increase for 5G cellular systems. A
promising multi-user access scheme, non-orthogonal multiple access (NOMA) with
successive interference cancellation (SIC), is currently under consideration.
In NOMA, spectrum efficiency is improved by allowing more than one user to
simultaneously access the same frequency-time resource and separating
multi-user signals by SIC at the receiver. These render resource allocation and
optimization in NOMA different from orthogonal multiple access in 4G. In this
paper, we provide theoretical insights and algorithmic solutions to jointly
optimize power and channel allocation in NOMA. For utility maximization, we
mathematically formulate NOMA resource allocation problems. We characterize and
analyze the problems' tractability under a range of constraints and utility
functions. For tractable cases, we provide polynomial-time solutions for global
optimality. For intractable cases, we prove the NP-hardness and propose an
algorithmic framework combining Lagrangian duality and dynamic programming
(LDDP) to deliver near-optimal solutions. To gauge the performance of the
obtained solutions, we also provide optimality bounds on the global optimum.
Numerical results demonstrate that the proposed algorithmic solution can
significantly improve the system performance in both throughput and fairness
over orthogonal multiple access as well as over a previous NOMA resource
allocation scheme.Comment: IEEE Transactions on Wireless Communications, revisio
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems
Constraint satisfaction problems (CSPs) are an important formal framework for
the uniform treatment of various prominent AI tasks, e.g., coloring or
scheduling problems. Solving CSPs is, in general, known to be NP-complete and
fixed-parameter intractable when parameterized by their constraint scopes. We
give a characterization of those classes of CSPs for which the problem becomes
fixed-parameter tractable.
Our characterization significantly increases the utility of the CSP framework
by making it possible to decide the fixed-parameter tractability of problems
via their CSP formulations.
We further extend our characterization to the evaluation of unions of
conjunctive queries, a fundamental problem in databases. Furthermore, we
provide some new insight on the frontier of PTIME solvability of CSPs.
In particular, we observe that bounded fractional hypertree width is more
general than bounded hypertree width only for classes that exhibit a certain
type of exponential growth.
The presented work resolves a long-standing open problem and yields powerful
new tools for complexity research in AI and database theory.Comment: Full and extended version of the IJCAI2020 paper with the same titl
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming
The NP-hard general factor problem asks, given a graph and for each vertex a
list of integers, whether the graph has a spanning subgraph where each vertex
has a degree that belongs to its assigned list. The problem remains NP-hard
even if the given graph is bipartite with partition U+V, and each vertex in U
is assigned the list {1}; this subproblem appears in the context of constraint
programming as the consistency problem for the extended global cardinality
constraint. We show that this subproblem is fixed-parameter tractable when
parameterized by the size of the second partite set V. More generally, we show
that the general factor problem for bipartite graphs, parameterized by |V|, is
fixed-parameter tractable as long as all vertices in U are assigned lists of
length 1, but becomes W[1]-hard if vertices in U are assigned lists of length
at most 2. We establish fixed-parameter tractability by reducing the problem
instance to a bounded number of acyclic instances, each of which can be solved
in polynomial time by dynamic programming.Comment: Full version of a paper that appeared in preliminary form in the
proceedings of IPEC'1
The Complexity of Planning Revisited - A Parameterized Analysis
The early classifications of the computational complexity of planning under
various restrictions in STRIPS (Bylander) and SAS+ (Baeckstroem and Nebel) have
influenced following research in planning in many ways. We go back and
reanalyse their subclasses, but this time using the more modern tool of
parameterized complexity analysis. This provides new results that together with
the old results give a more detailed picture of the complexity landscape. We
demonstrate separation results not possible with standard complexity theory,
which contributes to explaining why certain cases of planning have seemed
simpler in practice than theory has predicted. In particular, we show that
certain restrictions of practical interest are tractable in the parameterized
sense of the term, and that a simple heuristic is sufficient to make a
well-known partial-order planner exploit this fact.Comment: (author's self-archived copy
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