Walking Through Waypoints

We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set $\mathscr{W}\subseteq V$: the \emph{waypoints}. This waypoint routing problem finds immediate applications in the context of modern networked distributed systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial-time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable

An optimal construction of Hanf sentences

We give the first elementary construction of equivalent formulas in Hanf normal form. The triply exponential upper bound is complemented by a matching lower bound

Spatial intratumoral heterogeneity and temporal clonal evolution in esophageal squamous cell carcinoma.

Esophageal squamous cell carcinoma (ESCC) is among the most common malignancies, but little is known about its spatial intratumoral heterogeneity (ITH) and temporal clonal evolutionary processes. To address this, we performed multiregion whole-exome sequencing on 51 tumor regions from 13 ESCC cases and multiregion global methylation profiling for 3 of these 13 cases. We found an average of 35.8% heterogeneous somatic mutations with strong evidence of ITH. Half of the driver mutations located on the branches of tumor phylogenetic trees targeted oncogenes, including PIK3CA, NFE2L2 and MTOR, among others. By contrast, the majority of truncal and clonal driver mutations occurred in tumor-suppressor genes, including TP53, KMT2D and ZNF750, among others. Interestingly, phyloepigenetic trees robustly recapitulated the topological structures of the phylogenetic trees, indicating a possible relationship between genetic and epigenetic alterations. Our integrated investigations of spatial ITH and clonal evolution provide an important molecular foundation for enhanced understanding of tumorigenesis and progression in ESCC

The complexity of acyclic conjunctive queries revisited

In this paper, we consider first-order logic over unary functions and study the complexity of the evaluation problem for conjunctive queries described by such kind of formulas. A natural notion of query acyclicity for this language is introduced and we study the complexity of a large number of variants or generalizations of acyclic query problems in that context (Boolean or not Boolean, with or without inequalities, comparisons, etc...). Our main results show that all those problems are \textit{fixed-parameter linear} i.e. they can be evaluated in time $f(|Q|).|\textbf{db}|.|Q(\textbf{db})|$ where $|Q|$ is the size of the query $Q$, $|\textbf{db}|$ the database size, $|Q(\textbf{db})|$ is the size of the output and $f$ is some function whose value depends on the specific variant of the query problem (in some cases, $f$ is the identity function). Our results have two kinds of consequences. First, they can be easily translated in the relational (i.e., classical) setting. Previously known bounds for some query problems are improved and new tractable cases are then exhibited. Among others, as an immediate corollary, we improve a result of \~\cite{PapadimitriouY-99} by showing that any (relational) acyclic conjunctive query with inequalities can be evaluated in time $f(|Q|).|\textbf{db}|.|Q(\textbf{db})|$. A second consequence of our method is that it provides a very natural descriptive approach to the complexity of well-known algorithmic problems. A number of examples (such as acyclic subgraph problems, multidimensional matching, etc...) are considered for which new insights of their complexity are given.Comment: 30 page

Proving Looping and Non-Looping Non-Termination by Finite Automata

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic

MoPS: A Modular Protection Scheme for Long-Term Storage

Current trends in technology, such as cloud computing, allow outsourcing the storage, backup, and archiving of data. This provides efficiency and flexibility, but also poses new risks for data security. It in particular became crucial to develop protection schemes that ensure security even in the long-term, i.e. beyond the lifetime of keys, certificates, and cryptographic primitives. However, all current solutions fail to provide optimal performance for different application scenarios. Thus, in this work, we present MoPS, a modular protection scheme to ensure authenticity and integrity for data stored over long periods of time. MoPS does not come with any requirements regarding the storage architecture and can therefore be used together with existing archiving or storage systems. It supports a set of techniques which can be plugged together, combined, and migrated in order to create customized solutions that fulfill the requirements of different application scenarios in the best possible way. As a proof of concept we implemented MoPS and provide performance measurements. Furthermore, our implementation provides additional features, such as guidance for non-expert users and export functionalities for external verifiers.Comment: Original Publication (in the same form): ASIACCS 201