## What is/are Simple Paths?

Simple Paths - In comparison to solo bouts, the bouts of countersinging males had increased syntax diversity, with higher numbers of simple paths and transition types (but not syllable types) in comparison to solo song, which had high sequence consistency.^{[1]}We investigate decision and enumeration problems concerning the evaluation of RPQs under several semantics that have recently been considered: arbitrary paths, shortest paths, paths without node repetitions (simple paths), and paths without edge repetitions (trails).

^{[2]}It shows that when the boundary contains a single run, the set of minimum odd bond reconstructions are described by simple paths connecting the endpoints of either the black or white run.

^{[3]}The algorithm consists in properly selecting random simple paths in the graph and performing the proximal gradient algorithm over these simple paths.

^{[4]}A subgraph path division algorithm (SPDA) is proposed to get the most reliable maximum flow distribution, which avoid the negative impact of the number of simple paths and its bottleneck capacity.

^{[5]}One of the powerful forms of specifying label constraints is through regular expressions, and the resulting problem of reachability queries under regular simple paths (RSP) form the core of many practical graph query languages such as SPARQL from W3C, Cypher of Neo4J, Oracle's PGQL and LDBC's G-CORE.

^{[6]}We describe a general purpose algorithm for counting simple cycles and simple paths of any length $$\ell $$ℓ on a (weighted di)graph on N vertices and M edges, achieving an asymptotic running time of $$O\left( N+M+\big (\ell ^\omega +\ell \Delta \big ) |S_\ell |\right) $$ON+M+(ℓω+ℓΔ)|Sℓ|.

^{[7]}This paper formulates the problem of Linear Hotspot Detection on All Simple Paths (LHDA) which identifies hotspots from the complete set of simple paths enumerated from a given spatial network.

^{[8]}Routing policies instead of simple paths are treated as the subject of learning when real-time travel information is available, where a routing policy is defined as a contingency plan that maps realized traffic conditions to path choices.

^{[9]}Then independent simple paths have been identified from the chosen medium and complex path to reduce the complexity of reliability estimation.

^{[10]}In the third phase, TOPSIS is utilized to rank the simple routings, which are simple paths.

^{[11]}We present an O ( n 2 + n log n log ( m n ) + m log m ) time and O ( n 2 + m ) space algorithm for computing a simple path from s to t or reporting no simple paths exist, where n is the number of points of X and m is the number of vertices of P.

^{[12]}