40,381 research outputs found
The Complexity of Kings
A king in a directed graph is a node from which each node in the graph can be
reached via paths of length at most two. There is a broad literature on
tournaments (completely oriented digraphs), and it has been known for more than
half a century that all tournaments have at least one king [Lan53]. Recently,
kings have proven useful in theoretical computer science, in particular in the
study of the complexity of the semifeasible sets [HNP98,HT05] and in the study
of the complexity of reachability problems [Tan01,NT02].
In this paper, we study the complexity of recognizing kings. For each
succinctly specified family of tournaments, the king problem is known to belong
to [HOZZ]. We prove that this bound is optimal: We construct a
succinctly specified tournament family whose king problem is
-complete. It follows easily from our proof approach that the problem
of testing kingship in succinctly specified graphs (which need not be
tournaments) is -complete. We also obtain -completeness
results for k-kings in succinctly specified j-partite tournaments, , and we generalize our main construction to show that -completeness
holds for testing k-kingship in succinctly specified families of tournaments
for all
P-Selectivity, Immunity, and the Power of One Bit
We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is
not EXP/1-immune. That is, we prove that some infinite P-selective set has no
infinite EXP-time subset, but we also prove that every infinite P-selective set
has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so
fragile that it is pierced by a single bit of information.
The above claims follow from broader results that we obtain about the
immunity of the P-selective sets. In particular, we prove that for every
recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is
not \Pi_2^p/1-immune
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
Ionization state, excited populations and emission of impurities in dynamic finite density plasmas: I. The generalized collisional-radiative model for light elements
The paper presents an integrated view of the population structure and its role in establishing the ionization state of light elements in dynamic, finite density, laboratory and astrophysical plasmas. There are four main issues, the generalized collisional-radiative picture for metastables in dynamic plasmas with Maxwellian free electrons and its particularizing to light elements, the methods of bundling and projection for manipulating the population equations, the systematic production/use of state selective fundamental collision data in the metastable resolved picture to all levels for collisonal-radiative modelling and the delivery of appropriate derived coefficients for experiment analysis. The ions of carbon, oxygen and neon are used in illustration. The practical implementation of the methods described here is part of the ADAS Project
Credimus
We believe that economic design and computational complexity---while already
important to each other---should become even more important to each other with
each passing year. But for that to happen, experts in on the one hand such
areas as social choice, economics, and political science and on the other hand
computational complexity will have to better understand each other's
worldviews.
This article, written by two complexity theorists who also work in
computational social choice theory, focuses on one direction of that process by
presenting a brief overview of how most computational complexity theorists view
the world. Although our immediate motivation is to make the lens through which
complexity theorists see the world be better understood by those in the social
sciences, we also feel that even within computer science it is very important
for nontheoreticians to understand how theoreticians think, just as it is
equally important within computer science for theoreticians to understand how
nontheoreticians think
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