Orthogonal Vectors Indexing

In the recent years, intensive research work has been dedicated to prove conditional lower bounds in order to reveal the inner structure of the class P. These conditional lower bounds are based on many popular conjectures on well-studied problems. One of the most heavily used conjectures is the celebrated Strong Exponential Time Hypothesis (SETH). It turns out that conditional hardness proved based on SETH goes, in many cases, through an intermediate problem - the Orthogonal Vectors (OV) problem. Almost all research work regarding conditional lower bound was concentrated on time complexity. Very little attention was directed toward space complexity. In a recent work, Goldstein et al.[WADS \u2717] set the stage for proving conditional lower bounds regarding space and its interplay with time. In this spirit, it is tempting to investigate the space complexity of a data structure variant of OV which is called OV indexing. In this problem n boolean vectors of size clogn are given for preprocessing. As a query, a vector v is given and we are required to verify if there is an input vector that is orthogonal to it or not. This OV indexing problem is interesting in its own, but it also likely to have strong implications on problems known to be conditionally hard, in terms of time complexity, based on OV. Having this in mind, we study OV indexing in this paper from many aspects. We give some space-efficient algorithms for the problem, show a tradeoff between space and query time, describe how to solve its reporting variant, shed light on an interesting connection between this problem and the well-studied SetDisjointness problem and demonstrate how it can be solved more efficiently on random input

Data Structure Lower Bounds for Document Indexing Problems

We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower bounds that cannot be obtained in any other known model of computation with the current techniques. Often our lower bounds match the known space-query time trade-off curve and in fact for all the problems considered, there is a very good and reasonable match between the our lower bounds and the known upper bounds, at least for some choice of input parameters. The problems that we consider are set intersection queries (both the reporting variant and the semi-group counting variant), indexing a set of documents for two-pattern queries, or forbidden- pattern queries, or queries with wild-cards, and indexing an input set of gapped-patterns (or two-patterns) to find those matching a document given at the query time.Comment: Full version of the conference version that appeared at ICALP 2016, 25 page

The institutional forces that impact on the understanding of Corporate Social Responsibility (CSR) in the form of social partnerships in the Peruvian Mining industry

The purpose of this research is to examine the regulative, normative and cultural-cognitive elements under the New Institutional theory that have an impact on the understanding of Corporate Social Responsibility (CSR) and the development of social partnerships between peasant communities, mining companies and government in Peru. The literature review shows that New institutionalism theory is a suitable theoretical framework as it analyses these three elements of institutionalism that shape the logic of behaviour of Peruvian native and non-native people towards CSR, including: regulative, represented by law; normative, seen in value dimensions; and cultural-cognitive, seen in the symbols that represent reality. This research contributes to the wider CSR literature in developing countries from the Andean region by capturing the native peoples’ voices. To this end, multiple qualitative methods including observations and semi-structured interviews have been utilised as they allow for a more in-depth, exploratory study. In total, 53 semi-structured interviews were carried out between August 2016 and September 2017 in Ancash and Lima regions. Moreover, indigenous methodology has been deployed to identify the ontological and epistemological stances of native people that involved participating in their traditions and seeking understanding of their oral stories. The findings from this study regarding the regulative elements, indicate that, whilst in Peru there is no specific law that promotes social partnerships, the government has developed an ecosystem of law that promotes social partnerships. The Work for Taxes law is appointed as the most important legal tool that fosters early development of partnerships. Similarly, the Prior Consultation law permits a space for dialogue between comuneros and mining companies as a starting point of a partnership. However, there is the perception that it does not protect comuneros’ rights from Andean regions, but rather, only indigenous people from the Amazon. For this reason, comuneros have often resorted to protest, which they see as a legitimate way to change the law to protect their rights. The findings regarding the normative elements of institutionalism suggest that egalitarianism is the most important value dimension for the development of partnerships as it offers the opportunity for collaboration between the parties and promotes the comuneros’ common welfare. Moreover, mining companies need to increase their efforts to develop trust by developing CSR initiatives that will benefit peasant communities. Meanwhile, comuneros demonstrate two levels of ambition to access CSR initiatives, a community-wide ambition, on which they are seeking for the best outcome for their own community; and group ambition, on which comuneros pursue economic group goals. Finally, in respect of the cultural-cognitive elements, this study found that comuneros demand CSR to have both components: compulsory CSR on which its initiatives attend their urgent needs; and voluntary CSR aimed at developing their long-term capabilities. Moreover, partnerships have been changing from bilateral agreements between comuneros and mining companies, towards tripartite ones that include the participation of the government, which can provide the technical support in the development of CSR initiatives; meanwhile, third parties only occupy the role as an advisor in the execution of CSR initiatives

On the Hardness of Set Disjointness and Set Intersection with Bounded Universe

In the SetDisjointness problem, a collection of m sets S_1,S_2,...,S_m from some universe U is preprocessed in order to answer queries on the emptiness of the intersection of some two query sets from the collection. In the SetIntersection variant, all the elements in the intersection of the query sets are required to be reported. These are two fundamental problems that were considered in several papers from both the upper bound and lower bound perspective. Several conditional lower bounds for these problems were proven for the tradeoff between preprocessing and query time or the tradeoff between space and query time. Moreover, there are several unconditional hardness results for these problems in some specific computational models. The fundamental nature of the SetDisjointness and SetIntersection problems makes them useful for proving the conditional hardness of other problems from various areas. However, the universe of the elements in the sets may be very large, which may cause the reduction to some other problems to be inefficient and therefore it is not useful for proving their conditional hardness. In this paper, we prove the conditional hardness of SetDisjointness and SetIntersection with bounded universe. This conditional hardness is shown for both the interplay between preprocessing and query time and the interplay between space and query time. Moreover, we present several applications of these new conditional lower bounds. These applications demonstrates the strength of our new conditional lower bounds as they exploit the limited universe size. We believe that this new framework of conditional lower bounds with bounded universe can be useful for further significant applications

A polynomial Turing-kernel for weighted independent set in bull-free graphs

The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size k, when k is part of the instance. Our main result in this paper is to show the existence of an FPT algorithm when we parameterize the problem by the solution size k. A polynomial kernel is unlikely to exist for this problem. We show however that our problem has a polynomial size Turingkernel. More precisely, the hard cases are instances of size O(k5). As a byproduct, if we forbid odd holes in addition to the bull, we show the existence of a polynomial time algorithm for the stable set problem. We also prove that the chromatic number of a bull-free graph is bounded by a function of its clique number and the maximum chromatic number of its triangle-free induced subgraphs. All our results rely on a decomposition theorem for bull-free graphs due to Chudnovsky which is modified here, allowing us to provide extreme decompositions, adapted to our computational purpose

Approximating the edge length of 2-edge connected planar geometric graphs on a set of points

Given a set P of n points in the plane, we solve the problems of constructing a geometric planar graph spanning P 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set P, respectively. First, we construct in O(nlogn) time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in O(nlogn) time a 2-edge connected geometric planar graph spanning P with max edge length bounded by √5 times the optimal, assuming that the set P forms a connected Unit Disk Graph. Second, we prove that 2 times the optimal is always sufficient if the set of points forms a 2 edge connected Unit Disk Graph and give an algorithm that runs in O(n 2) time. We also show that for κ ∈ O(√n), there exists a set P of n points in the plane such that even though the Unit Disk Graph spanning P is κ-vertex connected, there is no 2-edge connected geometric planar graph spanning P even if the length of its edges is allowed to be up to 17/16