Maximizing Revenues for Online-Dial-a-Ride

In the classic Dial-a-Ride Problem, a server travels in some metric space to serve requests for rides. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that is earned if the request is satisfied. The goal is to serve requests within a time limit such that the total revenue is maximized. We first prove that the version of this problem where edges in the input graph have varying weights is NP-complete. We also prove that no algorithm can be competitive for this problem. We therefore consider the version where edges in the graph have unit weight and develop a 2-competitive algorithm for this problem

On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Max flow vitality in general and stst-planar graphs

The \emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after determining the vitality of arcs and/or nodes, and given a planar embedding of the graph, we can determine the vitality of a `contiguous' set of arcs/nodes in time proportional to the size of the set.Comment: 12 pages, 3 figure

On Approximating Restricted Cycle Covers

A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We come close to settling the complexity and approximability of computing L-cycle covers. On the one hand, we show that for almost all L, computing L-cycle covers of maximum weight in directed and undirected graphs is APX-hard and NP-hard. Most of our hardness results hold even if the edge weights are restricted to zero and one. On the other hand, we show that the problem of computing L-cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8/3 in the case of directed graphs. This holds for arbitrary sets L.Comment: To appear in SIAM Journal on Computing. Minor change

Apical endosomes isolated from kidney collecting duct principal cells lack subunits of the proton pumping ATPase.

Endocytic vesicles that are involved in the vasopressin-stimulated recycling of water channels to and from the apical membrane of kidney collecting duct principal cells were isolated from rat renal papilla by differential and Percoll density gradient centrifugation. Fluorescence quenching measurements showed that the isolated vesicles maintained a high, HgCl2-sensitive water permeability, consistent with the presence of vasopressin-sensitive water channels. They did not, however, exhibit ATP-dependent luminal acidification, nor any N-ethylmaleimide-sensitive ATPase activity, properties that are characteristic of most acidic endosomal compartments. Western blotting with specific antibodies showed that the 31- and 70-kD cytoplasmically oriented subunits of the vacuolar proton pump were not detectable in these apical endosomes from the papilla, whereas they were present in endosomes prepared in parallel from the cortex. In contrast, the 56-kD subunit of the proton pump was abundant in papillary endosomes, and was localized at the apical pole of principal cells by immunocytochemistry. Finally, an antibody that recognizes the 16-kD transmembrane subunit of oat tonoplast ATPase cross-reacted with a distinct 16-kD band in cortical endosomes, but no 16-kD band was detectable in endosomes from the papilla. This antibody also recognized a 16-kD band in affinity-purified H+ ATPase preparations from bovine kidney medulla. Therefore, early endosomes derived from the apical plasma membrane of collecting duct principal cells fail to acidify because they lack functionally important subunits of a vacuolar-type proton pumping ATPase, including the 16-kD transmembrane domain that serves as the proton-conducting channel, and the 70-kD cytoplasmic subunit that contains the ATPase catalytic site. This specialized, non-acidic early endosomal compartment appears to be involved primarily in the hormonally induced recycling of water channels to and from the apical plasma membrane of vasopressin-sensitive cells in the kidney collecting duct

On implicational bases of closure systems with unique critical sets

We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size of the binary part are also established. We introduce a K-basis of a general closure system, which is a refinement of the canonical basis of Duquenne and Guigues, and discuss a polynomial algorithm to obtain it. We study closure systems with the unique criticals and some of its subclasses, where the K-basis is unique. A further refinement in the form of the E-basis is possible for closure systems without D-cycles. There is a polynomial algorithm to recognize the D-relation from a K-basis. Thus, closure systems without D-cycles can be effectively recognized. While E-basis achieves an optimum in one of its parts, the optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into plenary talk on conference Universal Algebra and Lattice Theory, June 2012, Szeged, Hungary 29 pages and 2 figure

An Integrated Decision Support System for the Sustainable Reuse of the Former Monastery of “Ritiro del Carmine” in Campania Region

Nowadays, many public administrations have abandoned and underused heritage buildings due to a lack of public resources, although the effective contribution of cultural heritage as a driver and enabler of sustainable development is strongly recognized. Currently, investments in cultural heritage have multidimensional impacts (social, economic, historical, and cultural) and can contribute to increasing overall local productivity; improving the wellbeing of inhabitants; and attracting funding from the public, private, and private–social sectors. Lack of public resources has pushed local administrations to favor new forms of valorization of public property that can promote the “adaptive reuse” of historic buildings in order to preserve their social, historical, and cultural values. At the same time, administrations seek to stimulate the experimentation of new circular business, financing, and governance models in heritage conservation, creating synergies between multiple actors; reducing the use of resources; and regenerating values, knowledge, and capital. The objective of this paper is to propose an integrated evaluation model, based on multicriteria analysis, and a financial model to support the choice of an alternative reuse of an ancient monastery in the municipality of Mugnano in the Campania region in order to define a “shared strategy” based on a “bottom-up” approach. This starts from the needs of the local community but does not neglect the historical and cultural values of the heritage building, as well as the economic and financial feasibility. The positive results obtained show that the model proposed can be a useful decision support tool in environments characterized by high complexity such as cultural heritage sites, where the objective is to precisely highlight the elements that influence the dynamics of choice for building shared bottom-up development strategies

A novel approach to represent and compare RNA secondary structures

Structural information is crucial in ribonucleic acid (RNA) analysis and functional annotation; nevertheless, how to include such structural data is still a debated problem. Dot-bracket notation is the most common and simple representation for RNA secondary structures but its simplicity leads also to ambiguity requiring further processing steps to dissolve. Here we present BEAR (Brand nEw Alphabet for RNA), a new context-aware structural encoding represented by a string of characters. Each character in BEAR encodes for a specific secondary structure element (loop, stem, bulge and internal loop) with specific length. Furthermore, exploiting this informative and yet simple encoding in multiple alignments of related RNAs, we captured how much structural variation is tolerated in RNA families and convert it into transition rates among secondary structure elements. This allowed us to compute a substitution matrix for secondary structure elements called MBR (Matrix of BEAR-encoded RNA secondary structures), of which we tested the ability in aligning RNA secondary structures. We propose BEAR and the MBR as powerful resources for the RNA secondary structure analysis, comparison and classification, motif finding and phylogeny

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure