167 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Independent Sets in Elimination Graphs with a Submodular Objective
Maximum weight independent set (MWIS) admits a -approximation in
inductively -independent graphs and a -approximation in
-perfectly orientable graphs. These are a a parameterized class of graphs
that generalize -degenerate graphs, chordal graphs, and intersection graphs
of various geometric shapes such as intervals, pseudo-disks, and several
others. We consider a generalization of MWIS to a submodular objective. Given a
graph and a non-negative submodular function , the goal is to approximately solve where is the set of independent sets of . We obtain an
-approximation for this problem in the two mentioned graph
classes. The first approach is via the multilinear relaxation framework and a
simple contention resolution scheme, and this results in a randomized algorithm
with approximation ratio at least . This approach also yields
parallel (or low-adaptivity) approximations. Motivated by the goal of designing
efficient and deterministic algorithms, we describe two other algorithms for
inductively -independent graphs that are inspired by work on streaming
algorithms: a preemptive greedy algorithm and a primal-dual algorithm. In
addition to being simpler and faster, these algorithms, in the monotone
submodular case, yield the first deterministic constant factor approximations
for various special cases that have been previously considered such as
intersection graphs of intervals, disks and pseudo-disks.Comment: Extended abstract to appear in Proceedings of APPROX 2023. v2
corrects technical typos in few place
Indigenous Territorial Autonomy and Self-Government in the Diverse Americas
Across the Americas, Indigenous and Afro-descendent peoples have demanded autonomy, self-determination, and self-governance. By exerting their collective rights, they have engaged with domestic and international standards on the rights of Indigenous Peoples, implemented full-fledged mechanisms for autonomous governance, and promoted political and constitutional reform aimed at expanding understandings of multicultural citizenship and the plurinational state. Yet these achievements come in conflict with national governments’ adoption of neoliberal economic and neo-extractive policies which advance their interests over those of Indigenous communities.
Available for the first time in English, Indigenous Territorial Autonomy and Self-Government in the Diverse Americas explores current and historical struggles for autonomy within ancestral territories, experiences of self-governance in operation, and presents an overview of achievements, challenges, and threats across three decades. Case studies across Bolivia, Chile, Nicaragua, Peru, Colombia, Mexico, Panama, Ecuador, and Canada provide a detailed discussion of autonomy and self-governance in development and in practice.
Paying special attention to the role of Indigenous peoples’ organizations and activism in pursuing sociopolitical transformation, securing rights, and confronting multiple dynamics of dispossession, this book engages with current debates on Indigenous politics, relationships with national governments and economies, and the multicultural and plurinational state. This book will spark critical reflection on political experience and further exploration of the possibilities of the self-determination of peoples through territorial autonomies
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Sub-Exponential Lower Bounds for Branch-and-Bound with General Disjunctions via Interpolation
This paper investigates linear programming based branch-and-bound using
general disjunctions, also known as stabbing planes, for solving integer
programs. We derive the first sub-exponential lower bound (in the encoding
length of the integer program) for the size of a general branch-and-bound
tree for a particular class of (compact) integer programs, namely
for every . This is achieved by
showing that general branch-and-bound admits quasi-feasible monotone real
interpolation, which allows us to utilize sub-exponential lower-bounds for
monotone real circuits separating the so-called clique-coloring pair. One
important ingredient of the proof is that for every general branch-and-bound
tree proving integer-freeness of a product of two polytopes and
, there exists a closely related branch-and-bound tree for showing
integer-freeness of or one showing integer-freeness of . Moreover, we
prove that monotone real circuits can perform binary search efficiently
Efficient Algorithms and Hardness Results for the Weighted -Server Problem
In this paper, we study the weighted -server problem on the uniform metric
in both the offline and online settings. We start with the offline setting. In
contrast to the (unweighted) -server problem which has a polynomial-time
solution using min-cost flows, there are strong computational lower bounds for
the weighted -server problem, even on the uniform metric. Specifically, we
show that assuming the unique games conjecture, there are no polynomial-time
algorithms with a sub-polynomial approximation factor, even if we use
-resource augmentation for . Furthermore, if we consider the natural
LP relaxation of the problem, then obtaining a bounded integrality gap requires
us to use at least resource augmentation, where is the number of
distinct server weights. We complement these results by obtaining a
constant-approximation algorithm via LP rounding, with a resource augmentation
of for any constant .
In the online setting, an lower bound is known for the competitive
ratio of any randomized algorithm for the weighted -server problem on the
uniform metric. In contrast, we show that -resource augmentation can
bring the competitive ratio down by an exponential factor to only . Our online algorithm uses the two-stage approach of first
obtaining a fractional solution using the online primal-dual framework, and
then rounding it online.Comment: This paper will appear in the proceedings of APPROX 202
On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations
The strengthening of linear relaxations and bounds of mixed integer linear
programs has been an active research topic for decades. Enumeration-based
methods for integer programming like linear programming-based branch-and-bound
exploit strong dual bounds to fathom unpromising regions of the feasible space.
In this paper, we consider the strengthening of linear programs via a composite
of Dantzig-Wolfe and Fenchel decompositions. We provide geometric
interpretations of these two classical methods. Motivated by these geometric
interpretations, we introduce a novel approach for solving Fenchel sub-problems
and introduce a novel decomposition combining Dantzig-Wolfe and Fenchel
decompositions in an original manner. We carry out an extensive computational
campaign assessing the performance of the novel decomposition on the
unsplittable flow problem. Very promising results are obtained when the new
approach is compared to classical decomposition methods
Online Dynamic Acknowledgement with Learned Predictions
We revisit the online dynamic acknowledgment problem. In the problem, a
sequence of requests arrive over time to be acknowledged, and all outstanding
requests can be satisfied simultaneously by one acknowledgement. The goal of
the problem is to minimize the total request delay plus acknowledgement cost.
This elegant model studies the trade-off between acknowledgement cost and
waiting experienced by requests. The problem has been well studied and the
tight competitive ratios have been determined. For this well-studied problem,
we focus on how to effectively use machine-learned predictions to have better
performance.
We develop algorithms that perform arbitrarily close to the optimum with
accurate predictions while concurrently having the guarantees arbitrarily close
to what the best online algorithms can offer without access to predictions,
thereby achieving simultaneous optimum consistency and robustness. This new
result is enabled by our novel prediction error measure. No error measure was
defined for the problem prior to our work, and natural measures failed due to
the challenge that requests with different arrival times have different effects
on the objective. We hope our ideas can be used for other online problems with
temporal aspects that have been resisting proper error measures.Comment: To appear in INFOCOM 202
Middle-mile optimization for next-day delivery
We consider an e-commerce retailer operating a supply chain that consists of
middle- and last-mile transportation, and study its ability to deliver products
stored in warehouses within a day from customer's order time. Successful
next-day delivery requires inventory availability and timely truck schedules in
the middle-mile and in this paper we assume a fixed inventory position and
focus on optimizing the middle-mile. We formulate a novel optimization problem
which decides the departure of the last middle-mile truck at each (potential)
network connection in order to maximize the number of next-day deliveries. We
show that the respective \emph{next-day delivery optimization} is a
combinatorial problem that is -hard to approximate within
, hence every retailer
that offers one-day deliveries has to deal with this complexity barrier. We
study three variants of the problem motivated by operational constraints that
different retailers encounter, and propose solutions schemes tailored to each
problem's properties. To that end, we rely on greedy submodular maximization,
pipage rounding techniques, and Lagrangian heuristics. The algorithms are
scalable, offer optimality gap guarantees, and evaluated in realistic datasets
and network scenarios were found to achieve near-optimal results
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