Robust network optimization under polyhedral demand uncertainty is NP-hard

AbstractMinimum cost network design/dimensioning problems where feasibility has to be ensured w.r.t. a given (possibly infinite) set of scenarios of requirements form an important subclass of robust LP problems with right-hand side uncertainty. Such problems arise in many practical contexts such as Telecommunications, logistic networks, power distribution networks, etc. Though some evidence of the computational difficulty of such problems can be found in the literature, no formal NP-hardness proof was available up to now. In the present paper, this pending complexity issue is settled for all robust network optimization problems featuring polyhedral demand uncertainty, both for the single-commodity and multicommodity case, even if the corresponding deterministic versions are polynomially solvable as regular (continuous) linear programs. A new family of polynomially solvable instances is also discussed

An oil pipeline design problem

Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574

Compact versus noncompact LP formulations for minimizing convex Choquet integrals

AbstractWe address here the problem of minimizing Choquet Integrals (also known as “Lovász Extensions”) over solution sets which can be either polyhedra or (mixed) integer sets. Typical applications of such problems concern the search of compromise solutions in multicriteria optimization. We focus here on the case where the Choquet Integrals to be minimized are convex, implying that the set functions (or “capacities”) underlying the Choquet Integrals considered are submodular. We first describe an approach based on a large scale LP formulation, and show how it can be handled via the so-called column-generation technique. We next investigate alternatives based on compact LP formulations, i.e. featuring a polynomial number of variables and constraints. Various potentially useful special cases corresponding to well-identified subclasses of underlying set functions are considered: quadratic and cubic submodular functions, and a more general class including set functions which, up to a sign, correspond to capacities which are both (k+1)−additive and k-monotone for k≥3. Computational experiments carried out on series of test instances, including transportation problems and knapsack problems, clearly confirm the superiority of compact formulations. As far as we know, these results represent the first systematic way of practically solving Choquet minimization problems on solution sets of significantly large dimensions

TimeMachine: Timeline Generation for Knowledge-Base Entities

We present a method called TIMEMACHINE to generate a timeline of events and relations for entities in a knowledge base. For example for an actor, such a timeline should show the most important professional and personal milestones and relationships such as works, awards, collaborations, and family relationships. We develop three orthogonal timeline quality criteria that an ideal timeline should satisfy: (1) it shows events that are relevant to the entity; (2) it shows events that are temporally diverse, so they distribute along the time axis, avoiding visual crowding and allowing for easy user interaction, such as zooming in and out; and (3) it shows events that are content diverse, so they contain many different types of events (e.g., for an actor, it should show movies and marriages and awards, not just movies). We present an algorithm to generate such timelines for a given time period and screen size, based on submodular optimization and web-co-occurrence statistics with provable performance guarantees. A series of user studies using Mechanical Turk shows that all three quality criteria are crucial to produce quality timelines and that our algorithm significantly outperforms various baseline and state-of-the-art methods.Comment: To appear at ACM SIGKDD KDD'15. 12pp, 7 fig. With appendix. Demo and other info available at http://cs.stanford.edu/~althoff/timemachine

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Rostral and caudal pharyngeal arches share a common neural crest ground pattern

In vertebrates, face and throat structures, such as jaw, hyoid and thyroid cartilages develop from a rostrocaudal metameric series of pharyngeal arches, colonized by cranial neural crest cells (NCCs). Colinear Hox gene expression patterns underlie arch specific morphologies, with the exception of the first (mandibular) arch, which is devoid of any Hox gene activity. We have previously shown that the first and second (hyoid) arches share a common, Hox-free, patterning program. However, whether or not more posterior pharyngeal arch neural crest derivatives are also patterned on the top of the same ground-state remained an unanswered question. Here, we show that the simultaneous inactivation of all Hoxa cluster genes in NCCs leads to multiple jaw and first arch-like structures, partially replacing second, third and fourth arch derivatives, suggesting that rostral and caudal arches share the same mandibular arch-like ground patterning program. The additional inactivation of the Hoxd cluster did not significantly enhance such a homeotic phenotype, thus indicating a preponderant role of Hoxa genes in patterning skeletogenic NCCs. Moreover, we found that Hoxa2 and Hoxa3 act synergistically to pattern third and fourth arch derivatives. These results provide insights into how facial and throat structures are assembled during development, and have implications for the evolution of the pharyngeal region of the vertebrate head

A Multi-commodity network flow model for cloud service environments

Next-generation systems, such as the big data cloud, have to cope with several challenges, e.g., move of excessive amount of data at a dictated speed, and thus, require the investigation of concepts additional to security in order to ensure their orderly function. Resilience is such a concept, which when ensured by systems or networks they are able to provide and maintain an acceptable level of service in the face of various faults and challenges. In this paper, we investigate the multi-commodity flows problem, as a task within our D 2 R 2 +DR resilience strategy, and in the context of big data cloud systems. Specifically, proximal gradient optimization is proposed for determining optimal computation flows since such algorithms are highly attractive for solving big data problems. Many such problems can be formulated as the global consensus optimization ones, and can be solved in a distributed manner by the alternating direction method of multipliers (ADMM) algorithm. Numerical evaluation of the proposed model is carried out in the context of specific deployments of a situation-aware information infrastructure

Performance of field-emitting resonating carbon nanotubes as radio-frequency demodulators

International audienceWe report on a systematic study of the use of resonating nanotubes in a field emission (FE) configuration to demodulate radio frequency signals. We particularly concentrate on how the demodulation depends on the variation of the field amplification factor during resonance. Analytical formulas describing the demodulation are derived as functions of the system parameters. Experiments using AM and FM demodulations in a transmission electron microscope are also presented with a determination of all the pertinent experimental parameters. Finally we discuss the use of CNTs undergoing FE as nanoantennae and the different geometries that could be used for optimization and implementation. © 2011 American Physical Society

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers