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

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

Approximate solution of NP optimization problems

AbstractThis paper presents the main results obtained in the field of approximation algorithms in a unified framework. Most of these results have been revisited in order to emphasize two basic tools useful for characterizing approximation classes, that is, combinatorial properties of problems and approximation preserving reducibilities. In particular, after reviewing the most important combinatorial characterizations of the classes PTAS and FPTAS, we concentrate on the class APX and, as a concluding result, we show that this class coincides with the class of optimization problems which are reducible to the maximum satisfiability problem with respect to a polynomial-time approximation preserving reducibility

DIGITAL TECHNOLOGIES IN COMPLETE REMOVABLE DENTURE: A CASE SERIES

Aim: complete removable denture has been the last prosthetic procedure to follow the digitization because of drawbacks into the intraoral scans of edentulous arches; in addition, it is impossible to record muco-compressive impressions through IOS. So, a full digital procedure is not yet conceivable. We considered the possibility of an “hybrid” protocol thanks to a specific software. The hybrid protocol requires traditional techniques for the anatomical impression followed by laboratory scan of casts and wax. Methods: the software consists in two synergic programs: - Ruthinium Digital Preview allows to have a picture of the prosthetic project and change it previously, thanks to two calibrated photographs. - Ruthinium Denture Guide is a 3D software that helps laboratory work into denture production, particularly to a correct setting of acrylic teeth. The planned dental setting is printed in a template. Template and base plate, both 3D printed, are connected thanks to a structure that ensures the designed occlusal scheme. Results: the collected clinical cases did not allow a statistic analysis about patient and clinical satisfaction through evaluation questionnaires. Conclusion: it looks like that patients appreciate the prosthetic rehabilitation previsualization and in particular being actively involved in aesthetic choices. Clinically, it appears to be a shorter need for touch-ups at the last appointment; probably because of the 3D tooth position planning

Algorithmic aspects of disjunctive domination in graphs

For a graph $G=(V,E)$, a set $D\subseteq V$ is called a \emph{disjunctive dominating set} of $G$ if for every vertex $v\in V\setminus D$, $v$ is either adjacent to a vertex of $D$ or has at least two vertices in $D$ at distance $2$ from it. The cardinality of a minimum disjunctive dominating set of $G$ is called the \emph{disjunctive domination number} of graph $G$, and is denoted by $\gamma_{2}^{d}(G)$. The \textsc{Minimum Disjunctive Domination Problem} (MDDP) is to find a disjunctive dominating set of cardinality $\gamma_{2}^{d}(G)$. Given a positive integer $k$ and a graph $G$, the \textsc{Disjunctive Domination Decision Problem} (DDDP) is to decide whether $G$ has a disjunctive dominating set of cardinality at most $k$. In this article, we first propose a linear time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a $(\ln(\Delta^{2}+\Delta+2)+1)$-approximation algorithm for MDDP in general graphs and prove that MDDP can not be approximated within $(1-\epsilon) \ln(|V|)$ for any $\epsilon>0$ unless NP $\subseteq$ DTIME$(|V|^{O(\log \log |V|)})$. Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree $3$

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

Phosfinder: a web server for the identification of phosphate-binding sites on protein structures

Phosfinder is a web server for the identification of phosphate binding sites in protein structures. Phosfinder uses a structural comparison algorithm to scan a query structure against a set of known 3D phosphate binding motifs. Whenever a structural similarity between the query protein and a phosphate binding motif is detected, the phosphate bound by the known motif is added to the protein structure thus representing a putative phosphate binding site. Predicted binding sites are then evaluated according to (i) their position with respect to the query protein solvent-excluded surface and (ii) the conservation of the binding residues in the protein family. The server accepts as input either the PDB code of the protein to be analyzed or a user-submitted structure in PDB format. All the search parameters are user modifiable. Phosfinder outputs a list of predicted binding sites with detailed information about their structural similarity with known phosphate binding motifs, and the conservation of the residues involved. A graphical applet allows the user to visualize the predicted binding sites on the query protein structure. The results on a set of 52 apo/holo structure pairs show that the performance of our method is largely unaffected by ligand-induced conformational changes. Phosfinder is available at http://phosfinder.bio.uniroma2.it

The horizontal root fractures. Diagnosis, clinical management and three-year follow-up

Objective: The aim of this retrospective analysis is to describe and to evaluate the middle third horizontal root fractures, long term clinical management results and to estimate the effect of treatments factors upon healing and survival rate. Methods: Our clinical study included 42 patients presenting a middle third horizontal root fracture in permanent dentition. For each patient at t the parameters recorded were: diastasis, mobility, sensibility, periodontal inflammation, pulpal pathology, associated fracture and dislocation of the coronal fragment. The follow-up was performed after 6 (t1), 12 (t2) and 36 (t3) months after the trauma, both clinically and radiologically. Clinical examination, vitality tests and a radiological evaluation (periapical x-ray) were performed. Results: At t0 it was observed: diastasis (14, 3%), mobility (28, 6%), thermal sensibility (61, 9%), periodontal inflammation (4, 8%), pulpal pathology (38, 1%) and dislocation of the coronal fragment (47, 6%) of the patients. The treatment plan started with the coronal fragment repositioning and the blockage (splint) with the adjacent teeth in 47, 6% of cases. A root canal treatment was performed at t in 52,4% of the fractured teeth. Statistical analysis showed the highest level of significance between pulpal lesions (t) and associated fractures. The mobility, sensibility and pulpar lesions parameters, showed a reduction in relation to the follow up timing, with a main variation remarkably evident between t and t1. The ratio between observation time and the presence of diastasis was statistically significant. Conclusion: The analysis of the clinical results exhibits the high success rate of a conservative approach in the treatment of teeth fractured in the middle third of the root

The Use of Premixed Calcium Silicate Bioceramic Sealer with Warm Carrier-Based Technique: A 2-Year Study for Patients Treated in a Master Program

Background: Recently several calcium silicate flowable sealers have been introduced as endodontic materials for the root canal. This clinical study tested the use of a new premixed calcium silicate bioceramic sealer in association with the Thermafil warm carrier-based technique (TF). Epoxy-resin-based sealer with the warm carrier-based technique was the control group. Methodology: Healthy consecutive patients (n = 85) requiring 94 root canal treatments were enrolled in this study and assigned to one filling group (Ceraseal-TF n = 47, AH Plus-TF n = 47) in accordance with operator training and best clinical practice. Periapical X-rays were taken preoperatively, after root canal filling and after 6, 12 and 24 months. Two evaluators blindly assessed the periapical index (PAI) and sealer extrusion in the groups (k = 0.90). Healing rate and survival rate were also evaluated. Chi-square tests was used to analyze significant differences between the groups. Multilevel analysis was performed to evaluate the factors associated with healing status. Results: A total of 89 root canal treatments in 82 patients were analyzed at the end-line (24 months). The total drop-out was 3.6% (3 patients; 5 teeth). A total of 91.1% of healed teeth (PAI 1-2) was observed in Ceraseal-TF, with 88.6% in AH Plus-TF. No significant difference was observed on healing outcome and survival among the two filling groups (p > 0.05). Apical extrusion of the sealers occurred in 17 cases (19.0%). Of these, 6 occurred in Ceraseal-TF (13.3%) and 11 in AH Plus-TF (25.0%). Three Ceraseal extrusions were radiographically undetectable after 24 months. All the AH Plus extrusions did not change during the evaluation time. Conclusions: The combined use of the carrier-based technique and premixed CaSi-based bioceramic sealer showed clinical results comparable with carrier-based technique and epoxy-resin-based sealer. The radiographical disappearance of apically extruded Ceraseal is a possible event in the first 24 months