69,775 research outputs found
Quantitative games with interval objectives
Traditionally quantitative games such as mean-payoff games and discount sum
games have two players -- one trying to maximize the payoff, the other trying
to minimize it. The associated decision problem, "Can Eve (the maximizer)
achieve, for example, a positive payoff?" can be thought of as one player
trying to attain a payoff in the interval . In this paper we
consider the more general problem of determining if a player can attain a
payoff in a finite union of arbitrary intervals for various payoff functions
(liminf, mean-payoff, discount sum, total sum). In particular this includes the
interesting exact-value problem, "Can Eve achieve a payoff of exactly (e.g.)
0?"Comment: Full version of CONCUR submissio
Positional Determinacy of Games with Infinitely Many Priorities
We study two-player games of infinite duration that are played on finite or
infinite game graphs. A winning strategy for such a game is positional if it
only depends on the current position, and not on the history of the play. A
game is positionally determined if, from each position, one of the two players
has a positional winning strategy.
The theory of such games is well studied for winning conditions that are
defined in terms of a mapping that assigns to each position a priority from a
finite set. Specifically, in Muller games the winner of a play is determined by
the set of those priorities that have been seen infinitely often; an important
special case are parity games where the least (or greatest) priority occurring
infinitely often determines the winner. It is well-known that parity games are
positionally determined whereas Muller games are determined via finite-memory
strategies.
In this paper, we extend this theory to the case of games with infinitely
many priorities. Such games arise in several application areas, for instance in
pushdown games with winning conditions depending on stack contents.
For parity games there are several generalisations to the case of infinitely
many priorities. While max-parity games over omega or min-parity games over
larger ordinals than omega require strategies with infinite memory, we can
prove that min-parity games with priorities in omega are positionally
determined. Indeed, it turns out that the min-parity condition over omega is
the only infinitary Muller condition that guarantees positional determinacy on
all game graphs
Locally Self-Adjusting Skip Graphs
We present a distributed self-adjusting algorithm for skip graphs that
minimizes the average routing costs between arbitrary communication pairs by
performing topological adaptation to the communication pattern. Our algorithm
is fully decentralized, conforms to the model (i.e. uses
bit messages), and requires bits of memory for each
node, where is the total number of nodes. Upon each communication request,
our algorithm first establishes communication by using the standard skip graph
routing, and then locally and partially reconstructs the skip graph topology to
perform topological adaptation. We propose a computational model for such
algorithms, as well as a yardstick (working set property) to evaluate them. Our
working set property can also be used to evaluate self-adjusting algorithms for
other graph classes where multiple tree-like subgraphs overlap (e.g. hypercube
networks). We derive a lower bound of the amortized routing cost for any
algorithm that follows our model and serves an unknown sequence of
communication requests. We show that the routing cost of our algorithm is at
most a constant factor more than the amortized routing cost of any algorithm
conforming to our computational model. We also show that the expected
transformation cost for our algorithm is at most a logarithmic factor more than
the amortized routing cost of any algorithm conforming to our computational
model
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