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

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-line algorithms for polynomially solvable satisfiability problems

AbstractGiven a propositional Horn formula, we show how to maintain on-line information about its satisfiability during the insertion of new clauses. A data structure is presented which answers each satisfiability question in O(1) time and inserts a new clause of length q in O(q) amortized time. This significantly outperforms previously known solutions of the same problem. This result is extended also to a particular class of non-Horn formulae already considered in the literature, for which the space bound is improved. Other operations are considered, such as testing whether a given hypothesis is consistent with a satisfying interpretation of the given formula and determining a truth assignment which satisfies a given formula. The on-line time and space complexity of these operations is also analyzed

Query3d: a new method for high-throughput analysis of functional residues in protein structures

BACKGROUND: The identification of local similarities between two protein structures can provide clues of a common function. Many different methods exist for searching for similar subsets of residues in proteins of known structure. However, the lack of functional and structural information on single residues, together with the low level of integration of this information in comparison methods, is a limitation that prevents these methods from being fully exploited in high-throughput analyses. RESULTS: Here we describe Query3d, a program that is both a structural DBMS (Database Management System) and a local comparison method. The method conserves a copy of all the residues of the Protein Data Bank annotated with a variety of functional and structural information. New annotations can be easily added from a variety of methods and known databases. The algorithm makes it possible to create complex queries based on the residues' function and then to compare only subsets of the selected residues. Functional information is also essential to speed up the comparison and the analysis of the results. CONCLUSION: With Query3d, users can easily obtain statistics on how many and which residues share certain properties in all proteins of known structure. At the same time, the method also finds their structural neighbours in the whole PDB. Programs and data can be accessed through the PdbFun web interface

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