729 research outputs found
A near-optimal approximation algorithm for Asymmetric TSP on embedded graphs
We present a near-optimal polynomial-time approximation algorithm for the
asymmetric traveling salesman problem for graphs of bounded orientable or
non-orientable genus. Our algorithm achieves an approximation factor of O(f(g))
on graphs with genus g, where f(n) is the best approximation factor achievable
in polynomial time on arbitrary n-vertex graphs. In particular, the
O(log(n)/loglog(n))-approximation algorithm for general graphs by Asadpour et
al. [SODA 2010] immediately implies an O(log(g)/loglog(g))-approximation
algorithm for genus-g graphs. Our result improves the
O(sqrt(g)*log(g))-approximation algorithm of Oveis Gharan and Saberi [SODA
2011], which applies only to graphs with orientable genus g; ours is the first
approximation algorithm for graphs with bounded non-orientable genus.
Moreover, using recent progress on approximating the genus of a graph, our
O(log(g) / loglog(g))-approximation can be implemented even without an
embedding when the input graph has bounded degree. In contrast, the
O(sqrt(g)*log(g))-approximation algorithm of Oveis Gharan and Saberi requires a
genus-g embedding as part of the input.
Finally, our techniques lead to a O(1)-approximation algorithm for ATSP on
graphs of genus g, with running time 2^O(g)*n^O(1)
Constant-factor approximations for asymmetric TSP on nearly-embeddable graphs
In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a
closed walk of minimum cost in a directed graph visiting every vertex. We
consider the approximability of ATSP on topologically restricted graphs. It has
been shown by [Oveis Gharan and Saberi 2011] that there exists polynomial-time
constant-factor approximations on planar graphs and more generally graphs of
constant orientable genus. This result was extended to non-orientable genus by
[Erickson and Sidiropoulos 2014].
We show that for any class of \emph{nearly-embeddable} graphs, ATSP admits a
polynomial-time constant-factor approximation. More precisely, we show that for
any fixed , there exist , such that ATSP on
-vertex -nearly-embeddable graphs admits a -approximation in time
. The class of -nearly-embeddable graphs contains graphs with at
most apices, vortices of width at most , and an underlying surface
of either orientable or non-orientable genus at most . Prior to our work,
even the case of graphs with a single apex was open. Our algorithm combines
tools from rounding the Held-Karp LP via thin trees with dynamic programming.
We complement our upper bounds by showing that solving ATSP exactly on graphs
of pathwidth (and hence on -nearly embeddable graphs) requires time
, assuming the Exponential-Time Hypothesis (ETH). This is
surprising in light of the fact that both TSP on undirected graphs and Minimum
Cost Hamiltonian Cycle on directed graphs are FPT parameterized by treewidth
Adaptive Knobs for Resource Efficient Computing
Performance demands of emerging domains such as artificial intelligence, machine learning and vision, Internet-of-things etc., continue to grow. Meeting such requirements on modern multi/many core systems with higher power densities, fixed power and energy budgets, and thermal constraints exacerbates the run-time management challenge. This leaves an open problem on extracting the required performance within the power and energy limits, while also ensuring thermal safety. Existing architectural solutions including asymmetric and heterogeneous cores and custom acceleration improve performance-per-watt in specific design time and static scenarios. However, satisfying applications’ performance requirements under dynamic and unknown workload scenarios subject to varying system dynamics of power, temperature and energy requires intelligent run-time management.
Adaptive strategies are necessary for maximizing resource efficiency, considering i) diverse requirements and characteristics of concurrent applications, ii) dynamic workload variation, iii) core-level heterogeneity and iv) power, thermal and energy constraints. This dissertation proposes such adaptive techniques for efficient run-time resource management to maximize performance within fixed budgets under unknown and dynamic workload scenarios. Resource management strategies proposed in this dissertation comprehensively consider application and workload characteristics and variable effect of power actuation on performance for pro-active and appropriate allocation decisions. Specific contributions include i) run-time mapping approach to improve power budgets for higher throughput, ii) thermal aware performance boosting for efficient utilization of power budget and higher performance, iii) approximation as a run-time knob exploiting accuracy performance trade-offs for maximizing performance under power caps at minimal loss of accuracy and iv) co-ordinated approximation for heterogeneous systems
through joint actuation of dynamic approximation and power knobs for performance guarantees with minimal power consumption.
The approaches presented in this dissertation focus on adapting existing mapping techniques, performance boosting strategies, software and dynamic approximations to meet the performance requirements, simultaneously considering system constraints. The proposed strategies are compared against relevant state-of-the-art run-time management frameworks to qualitatively evaluate their efficacy
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations
This paper introduces a new mobile sensor scheduling problem, involving a
single robot tasked with monitoring several events of interest that occur at
different locations. Of particular interest is the monitoring of transient
events that can not be easily forecast. Application areas range from natural
phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano
using a ground robot) to urban activities ({\em e.g.}, monitoring early
formations of traffic congestion using an aerial robot). Motivated by those and
many other examples, this paper focuses on problems in which the precise
occurrence times of the events are unknown {\em a priori}, but statistics for
their inter-arrival times are available. The robot's task is to monitor the
events to optimize the following two objectives: {\em (i)} maximize the number
of events observed and {\em (ii)} minimize the delay between two consecutive
observations of events occurring at the same location. The paper considers the
case when a robot is tasked with optimizing the event observations in a
balanced manner, following a cyclic patrolling route. First, assuming the
cyclic ordering of stations is known, we prove the existence and uniqueness of
the optimal solution, and show that the optimal solution has desirable
convergence and robustness properties. Our constructive proof also produces an
efficient algorithm for computing the unique optimal solution with time
complexity, in which is the number of stations, with time
complexity for incrementally adding or removing stations. Except for the
algorithm, most of the analysis remains valid when the cyclic order is unknown.
We then provide a polynomial-time approximation scheme that gives a
-optimal solution for this more general, NP-hard problem
Traveling Salesman Problem
The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance
- …