9,939 research outputs found
Scheduling Bidirectional Traffic on a Path
We study the fundamental problem of scheduling bidirectional traffic along a
path composed of multiple segments. The main feature of the problem is that
jobs traveling in the same direction can be scheduled in quick succession on a
segment, while jobs in opposing directions cannot cross a segment at the same
time. We show that this tradeoff makes the problem significantly harder than
the related flow shop problem, by proving that it is NP-hard even for identical
jobs. We complement this result with a PTAS for a single segment and
non-identical jobs. If we allow some pairs of jobs traveling in different
directions to cross a segment concurrently, the problem becomes APX-hard even
on a single segment and with identical jobs. We give polynomial algorithms for
the setting with restricted compatibilities between jobs on a single and any
constant number of segments, respectively
Computing Socially-Efficient Cake Divisions
We consider a setting in which a single divisible good ("cake") needs to be
divided between n players, each with a possibly different valuation function
over pieces of the cake. For this setting, we address the problem of finding
divisions that maximize the social welfare, focusing on divisions where each
player needs to get one contiguous piece of the cake. We show that for both the
utilitarian and the egalitarian social welfare functions it is NP-hard to find
the optimal division. For the utilitarian welfare, we provide a constant factor
approximation algorithm, and prove that no FPTAS is possible unless P=NP. For
egalitarian welfare, we prove that it is NP-hard to approximate the optimum to
any factor smaller than 2. For the case where the number of players is small,
we provide an FPT (fixed parameter tractable) FPTAS for both the utilitarian
and the egalitarian welfare objectives
The Lazy Bureaucrat Scheduling Problem
We introduce a new class of scheduling problems in which the optimization is
performed by the worker (single ``machine'') who performs the tasks. A typical
worker's objective is to minimize the amount of work he does (he is ``lazy''),
or more generally, to schedule as inefficiently (in some sense) as possible.
The worker is subject to the constraint that he must be busy when there is work
that he can do; we make this notion precise both in the preemptive and
nonpreemptive settings. The resulting class of ``perverse'' scheduling
problems, which we denote ``Lazy Bureaucrat Problems,'' gives rise to a rich
set of new questions that explore the distinction between maximization and
minimization in computing optimal schedules.Comment: 19 pages, 2 figures, Latex. To appear, Information and Computatio
The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control
Much work has been devoted, during the past twenty years, to using complexity
to protect elections from manipulation and control. Many results have been
obtained showing NP-hardness shields, and recently there has been much focus on
whether such worst-case hardness protections can be bypassed by frequently
correct heuristics or by approximations. This paper takes a very different
approach: We argue that when electorates follow the canonical political science
model of societal preferences the complexity shield never existed in the first
place. In particular, we show that for electorates having single-peaked
preferences, many existing NP-hardness results on manipulation and control
evaporate.Comment: 38 pages, 2 figure
Energy-efficient algorithms for non-preemptive speed-scaling
We improve complexity bounds for energy-efficient speed scheduling problems
for both the single processor and multi-processor cases. Energy conservation
has become a major concern, so revisiting traditional scheduling problems to
take into account the energy consumption has been part of the agenda of the
scheduling community for the past few years.
We consider the energy minimizing speed scaling problem introduced by Yao et
al. where we wish to schedule a set of jobs, each with a release date, deadline
and work volume, on a set of identical processors. The processors may change
speed as a function of time and the energy they consume is the th power
of its speed. The objective is then to find a feasible schedule which minimizes
the total energy used.
We show that in the setting with an arbitrary number of processors where all
work volumes are equal, there is a approximation algorithm, where
is the generalized Bell number. This is the first constant
factor algorithm for this problem. This algorithm extends to general unequal
processor-dependent work volumes, up to losing a factor of
in the approximation, where is the maximum
ratio between two work volumes. We then show this latter problem is APX-hard,
even in the special case when all release dates and deadlines are equal and
is 4.
In the single processor case, we introduce a new linear programming
formulation of speed scaling and prove that its integrality gap is at most
. As a corollary, we obtain a
approximation algorithm where there is a single processor, improving on the
previous best bound of
when
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